Can I carry £25 in cash to UK without a receipt?

If anything, you're going to be questioned as to why you have only 25 pounds. Unless you look extremely suspicious, nobody's going to ask about the money's origin until you get well into the thousands.

Countries that set their exchange rates away from the market rate generally require that you only trade with official sources and that you don't take currency in/out of the country.

However, countries that do not mess with the exchange rates have no such restrictions, nobody cares about currency being carried across borders until it reaches quantities that suggest illegal activity is going on.

The British Pound is an example of the latter, nobody is going to give a hoot about 25 pounds. Off the top of my head the Euro, Canadian Dollar, Australian Dollar and Japanese Yen are likewise hard currencies. I'm sure New Zealand is also but I forget their currency unit. Beyond that my knowledge is way too out of date to say what other countries have hard currencies.

(Since there has been question about the term "hard currency"--hard currencies are currencies where the government doesn't decree what the exchange rate is, it's market price. A private seller will offer about the same rate as the government, there's no concept of unauthorized trades. Private trades exist on a small scale in areas dealing with tourists--it is not uncommon for shops near a border to accept the currency on the other side of the border.)

While it was not UK, this might still be relevant.

While I was traveling to Germany on my new passport for the first time, I was detained for several minutes when I couldn't reproduce my return flight. I was then asked how much money I have on me. It was if I recall correctly €400. I was also asked to produce the money so the border police can verify it. I was even asked to spread the bills so that he can count, he said he is not allowed to touch them. I know this was a cascade of mistakes on my part, I should be carrying my old passport along with a printed return ticket. If I hadn't done these mistakes, my cash wouldn't even be asked.

As long as you have a support letter or reservations and a return ticket, I don't think anyone would ask you how much cash you have on you. If you state that you have £25 without being asked, you will either be laughed at or will be assumed to act suspiciously.

In several circumstances that I entered UK, I was asked to translate for some Turkish visitors (although I am not a sworn translator). In none of those occasions, I ever heard of the amount of cash the visitors have on their person.

I hope this helps.