I would not suggest bringing animals abroad - either in carry on case or in the hold, a trans-Atlantic trip is a long journey for an animal and in the UK, that will be your one item of carry-on. But if you really must you need to start planning WELL ahead of time.
The regulations do change, and only certain airlines will carry animals. Also, the rules can vary between countries so you may have issues crossing borders between the UK, Ireland and the rest of Europe. So you need to find out what the regulations are for each country, and make sure that your dogs will be able to cross borders and the airlines/trains you are intending to use will allow them.
The Pet Travel Scheme regs can be read here: http://www.defra.gov.uk/animalh/quarantine/pets/index.htm
Honestly, I think they'd be much happier with a doggie-sitter back home.