I would certainly not plan on cycling. Ireland might be a different story - I know they have cycling tours of Ireland. But in Britain the roads are often very narrow with no real shoulder. And around London and the big cities there is a lot of traffic. Don't do it. I've traveled in Britain on the coaches/buses and they are probably your cheapest bet. They do go to some out of the way places, but schedules might be a problem. I used National Express a couple of years ago and it was fine and not to expensive relative to other modes of transport. There's also something called Citilink, I think. Oh the other problem with cycling is that it often rains a lot.