Do British citizens need a passport to visit the Republic of Ireland?

As you are a British citizen who was born in the UK, you don't need a passport to travel to the Republic of Ireland, as long as you have another form of photographic ID (for example a photo driving licence). The same applies for Irish citizens travelling to the UK, but not for any other nationality.

(Note that these are immigration requirements, and your airline may impose different requirements (eg Ryanair requires a passport, passport card or EU national ID card).)

The FlyBe website says:

British and Irish citizens must have a form of photographic ID which proves their nationality/citizenship for immigration purposes e.g. a valid passport or fulll/provisional photographic driving licence. (source: http://www.flybe.com/checkin/id-requirements.htm)

The Foreign Office also states that it's best to take a passport if you weren't born in the UK:

British nationals travelling from the UK don’t need a passport to visit Ireland. However, Irish immigration officers will check the ID of all passengers arriving by air from the UK and may ask for proof of nationality, particularly if you were born outside the UK. You are therefore advised to take your British passport with you. (source: https://www.gov.uk/foreign-travel-advice/ireland/entry-requirements)

As per Timatic, the database used by airlines:

Passport exemptions: Passengers with an official photo ID proving nationality issued to British nationals for travel between Ireland (Rep.) and Great Britain and Northern Ireland only.

Ironically, no British photo ID other than the passport proves nationality.

In practice, however, virtually all airlines, including FlyBe, accept UK driving licences, as stated on FlyBe's website.

At Irish immigration, simply present your boarding pass and driving licence, and you should have no problems.

British citizens of obviously non-British origin (such as those with another country of birth as stated on the UK driving licence) should present a UK birth/naturalisation certificate in addition to their UK driving licence, as these documents combined prove identity and nationality.

You can, if you are lucky. My nan once flew from Newcastle to Dublin with only her bus pass, but she was always lucky. There are two different questions here, 1) will you get through immigration, and 2) will you be allowed on the plane.

Immigration does not require a passport for an Irish citizen travelling to the UK or for a UK citizen travelling to Ireland, but you will have to be able to prove you are a citizen of Ireland or the UK. If you are white skinned and have a recognizable regional accent (as my nan did) then almost any official looking document with a photo on it may be enough. And while there is no active racial discriminatory policy on either side any more, the further you are from that ideal, the stronger the evidence for citizenship you may require.

Airlines usually demand proof of Id between booking the flight and issuing your boarding card. If you don't mind paying a few extra quid for peace of mind, have a chat with a travel agent before you make your final plans. They should be able to sort you out.

From the GOV.UK site about travelling to Ireland:

British nationals travelling from the UK don’t need a passport to visit Ireland. However, Irish immigration officers will check the ID of all passengers arriving by air from the UK and may ask for proof of nationality, particularly if you were born outside the UK. You are therefore advised to take your British passport with you.

So if you were born in the UK, then you should be okay, otherwise you might need to give them additional proof. Your passport, especially if it only has been recently expired might be okay.

Alternatively you can fly to Northern Ireland first, and use land transport to get to Ireland, as there is no border control, although you should still have a proper ID with you.

For domestic air travels ID requirements are much more relaxed. You can use a British Driving licence as an ID (and for domestic travels it is also acceptable if you are not actually a British Citizen, I used it multiple times for intra-UK travel - although once I had to fight the Ryanair attendant and show them their own rules). FlyBe has similar rules for domestic air travel:

Domestic travel:

• A valid passport
• An expired passport (domestic flights only up to two years after expiry)
• Valid driving licence (Full or Provisional are accepted)

(...)