Hi

Flying full service carriers in Europe is very expensive, and as you have identiifed, there are no Skyteam airlines based in the UK. The best way of getting to either EDI or DUB is with either www.easyjet.com or www.ryanair.com. Both fly from Stansted which is north east of London and is a huge hub for low cost carriers, second choice would be Luton which is also a huge hub for Easyjet.

The train is very interesting and scenic, but may take you five hours from London to Edinburgh and can prove expensive unless you do your homework with learning how to use the pesky ticket schemes they have set up.

Obviously, the only (realistic) way of getting from London to Dublin is to fly.