You can just say 'Hi, I only speak English, sorry.'

You can expand that a little to the situation by adding 'good morning' or whatever is right for the time of the day, either in English or if you know it in the local language. And keep your English accent strong for that.

Almost everybody in Europe will understand that and for those who don't you made clear there is a language barrier.

On the other hand, if you have time and the other person is willing to try, you might find you can communicate, if with a lot of guesses.

I am Dutch and have often traveled in places where I did not know the language, I survived.

Alternatively, you could learn a couple of phrases in German/Dutch/etc. like 'Hello, sorry I do not speak German/Dutch/etc. Do you speak English?' This is my tactics that does not require much effort :)

The polite way is to learn the phrase for "Sorry, I don't understand, do you speak English, please?" in the local language ("Entschuldigung, ich verstehe nicht, sprechen Sie Englisch, bitte?" in German, no idea in other languages) followed by "I'm sorry, do you speak English?" when they inevitable fail to understand your terrible pronunciation (from experience).

But, if you're travelling around a lot learning even a few phrases in the local language (especially if it is a country you're just passing through) is a big ask, then I'd go for "I'm sorry, do you speak English?" combined with an apologetic expression.

Generally speaking, the more you can manage in the local language the better and the more polite, but people are usually friendly to people who try their best. Try and learn the word for "sorry" in the native language if you can, then follow that by "Do you speak English?", and look apologetic for not understanding their language.

Ideally, learn how to say Sorry, I don't speak [language] in the local language. This is a simple phrase and so it is possible to learn it before travelling by listening to pre-recordings. Even if you pronounce it poorly, that is fine since you are expressing you do not speak it. After that, follow it with Do you speak English? which allows the other person to switch unless they are among those that don't.

The second approach is to just say: Sorry, English only. It is a broken sentence but that will do since there is clearly a language barrier. It helps to support the statement with an non-verbal expression of misunderstanding (raised shoulders, wide eyes for example).

Try to respond quickly and show your lack of understanding early as I've heard people tell me long stories before finally realizing that I did not understand anything they have been saying for several minutes! If that happens, just be apologetic, saying sorry either in English or the local language. While embarrassing yourself if uncomfortable, it is better to avoid embarrassing others. This is bound to be part of the travel experience.

Having lived in The Netherlands for two years my go-to if I do not understand a question is always:

"I'm sorry, I don't speak Dutch. Can we continue in English?"

For very simple interactions such as at the supermarket I will reply in basic Dutch, but often when I understand a question in Dutch I will just answer in English. I find that almost everyone I speak to would rather we immediately begin speaking in English than trying to communicate through my broken Dutch and I have never experienced someone reacting poorly to that. Of course you may find that it's not as simple in other countries that don't have as many fluent English speakers as The Netherlands.

Of course, it is good to be polite and this includes recognizing that English may not be the other person's first language. However, beyond that, I don't think that there is any one size fits all answer. A little research can help. Here are some of my experiences in attempting this.

In Denmark, especially Copenhagen, the standard of English is so high that I feel that people are even slightly offended when I ask "Do you speak English?" whether I do it in English or bad Danish. So, I have stopped doing this unless there is some reason to doubt the other person's ability. I had an amusing experience when checking in at Copenhagen airport once: the agent said: "Forstå du dansk?", I replied "Nej". She gave a little puzzled smile and switched to perfect English.

Netherlands, especially Amsterdam, is similar but with the extra twist that it is quite likely that the other person does not speak Dutch either. Once I attempted Dutch in a restaurant and the waitress replied: "sorry, I don't speak Dutch, I am Lithuanian".

The next factor that I look for is whether it is common for foreigners to learn the local language. Examples are: France, Germany, Spain, and Italy. In these cases, people are more used to hearing their own language spoken badly and will probably at least realise that you are trying to speak it. So, I attempt to learn a few basic phrases including "do you speak English?".

Next, be more careful when there are multiple local languages. Belgium is complex and you should look for clues as to whether you are in a French speaking area before attempting French. This also applies to Spain, if you are in a Catalan speaking area then recognizing that is appreciated, see next case.

You are in country or region where few foreigners attempt to learn the language. This can be challenging since, unless you have significant linguistic skills, the other person might not realize that you are attempting to speak their language. Once in Barcelona, I tried to learn a few basic Catalan phrases but I failed miserably. I don't think that people realized that I was even trying to speak their language. I know some Spanish (or rather Castilian) but I get the feeling that assuming that someone speaks Castilian is almost as bad as assuming that they speak English. I finally settled on saying in Castilian: "I am sorry, I don't speak Catalan, do you speak Castilian?". The answer was always yes but I got a much better reception than just assuming it. Note my use of Castilian for what English speakers commonly call Spanish. Recognizing that Castilian is not the only language in Spain also helps.

Portugal is an intermediate case. I have some success with simple Portuguese but also some Catalan like failures.

In these cases, you may as well just stick to English but be as polite as you can be. If you know some alternative language then it might help e.g. many Portuguese people know French. Of course, don't assume that but try it if you can.

All of those examples are European but the same applies elsewhere.

Quite a few foreigners attempt to learn Thai. Not many get very far but it is common enough that they will probably realize that you are trying and they may recognize your badly spoken simple phrases.

The same in Malaysia though you have the Belgium type problem that the native language of many is Chinese.

In Cambodia, few foreigners attempt to learn Khmer so unless you are very good at languages, they might not realize that you are trying to speak it.

China is a nice case. Enough foreigners attempt Mandarin that they might realize that you are trying. You can get an amazing positive reaction with just a few simple phrases. Not so for Cantonese though and there are yet other forms of Chinese. Attempting Mandarin in Hong Kong is rather like Spanish in Barcelona.

Finally the Philippines is another case. They usually recognize that you are trying to speak Tagalog but they are so unused to hearing it spoken badly that they are liable to collapse in laughter.

I was fortunate enough to be able to travel throughout Europe during my semester abroad. I'm also a polyglot and didn't have much trouble communicating in other countries, but I see how this can be a challenge. When I was in Germany, I was, for the first time there, out of my element because I do not speak German.

What I found to be helpful was, before going to an area where English is not the standard, memorise and practice the phrases for 'I'm sorry. I speak English' and 'Do you speak English?'. Here's a cheat-sheet for some of the more common languages in the world that I speak and can realistically help with (pronunciations are available online):

Spanish: Lo siento. Solo hablo inglés. // ¿Habla usted inglés?

French: Je suis desolé(e). Je parle seulement l'anglais. // Parlez-vous l'anglais ?

Portuguese: Eu o sento. Sô falo o inglês. // Fala você o inglês?

Arabic: ??? ???. ?? ???? ????????. // ???? ?????????

Those, along with some other basic words like 'Food', 'Water', 'House', 'Bed', 'Bathroom', 'Help', 'Please', 'Thank you', and 'Where' are among the words that I would emphasise knowing. Even if you don't know the language, somebody would understand if you came up and said something to the effect of 'Where food?' or 'Where bathroom?' or 'Help!'. Even if you can't communicate specifics ('I would like to dine in your finest five-star restaurant. Where might one find that?' or 'Could you direct me to the facilities?' or 'Help! I just witnessed a car crash and I think there are people that need help inside!'), those words will be enough to get people to understand that (a) you don't speak the language thus will need to be spoken to slowly or in another means (with a lot of gestures, visual aids, &c) and (b) get your point across enough that person knows what you're looking for.

I hope this was helpful!

English?

Most people you interact with will recognize the question immediately and either nod, often with a 'yes' to confirm, or shake their head for no.

If they shake their head, you can then frown and look down. This is a fairly universal indication that you are now 'stuck' for communicating and usually implies due to language, especially since you just offered English. A verbal 'hmmm' may also be used at this point.

The two advantages to this are that you don't need to learn the sentence in other languages and that you don't give the impression that you know some of the language by knowing the sounds in one sentence.

'Sorry, I don't speak your language.' is a good way to start.

Offering language alternatives (in that language), that you can speak, can be added when applicable.

If you have a minimal vocabulary, try to express that in that language ('I don't speak your language very well...').

Many people have experience in speaking with children and will attempt to adapt to a level that will work.