Day1/Day2 - London Day3- fly from london to edinburgh day3/4 edinburgh day 5 - flight from edinburgh to bristol. train from bristol to bath. day 5/6 - bath
day 7 - train to london. what is the approx cost i should expect for flights to edinburgh? are the connections from bristol to bath frequent?
I would seriously consider trains. The routes you are looking at are fast and frequent. I would not bother with the airports and the security hassles. You might even save some money by getting a Brit Rail Pass.