http://www.ukba.homeoffice.gov.uk/cu...montravelarea/
The UK does not make routine immigration checks on passenger travel within the CTA, and passengers are not required to carry a passport or national identity document for immigration purposes. [...]
However, there are exceptions to this principle - for example, a visa national will need to have a visa if they enter the UK from another part of the CTA.
There is no requirement for
any ID to travel between the Republic of Ireland & the UK (but there is the strange situation where you don't need ID
unless you do, which makes enforcement a bit tricky).
BA will only require ID if you check in baggage. That can even be your Executive Club card, and your driving licence should be fine. Some other airlines require ID for you to travel, but this is an airline, not an immigration, requirement.
You might find some more information in this recent thread;
http://www.flyertalk.com/forum/briti...ht-dublin.html