Learning to fly is a great hobby and your aspiration to fly into Europe the dream of many pilots. Flying is an expensive hobby and I'm based at Fairoaks in Surrey where you can get to Le Touquet, Channel Islands, Normandy etc within an hour. From Edinburgh, you'd need to add about 4 hours each way just to get to the south coast at typical light plane cruise speeds. For a return trip at club rates or a group share, you're looking at somewhere between £700~£1,200 just to get to the south coast of England.
I'd say that was fairly prohibitive. The flip side is I'd love to fly to Scotland and admire the views, spend a weekend on Islay or in the Highlands, but it's beyond my budget when I can get to France in a fraction of the time.
The second issue is the weather. Being fairly far north, the UK often suffers from large weather differences over a relatively short distance. For a new PPL (ie good VMC weather) to hope to fly a 500-600nm trip due south without encountering marginal weather enroute is very unlikely for most of the year I'm afraid.
Certainly learn to fly, enjoy the new skill, but make the most of what you have within a hour of your base as going further afield will certainly eat up that cash!
I may have made the wrong assumption that you want to fly yourself from Edinburgh to Europe. The other options open to you once you have your licence is to jump on a cheap commercial flight "darn sarf" and rent from a school nearer to the coast for your cross channel checkout and enjoy that foreign trip without the sweat and a lot less cost. Alternatively, get an FAA licence based on your UK PPL and take a trip to the USA where flying is a lot more fun, much more accessible and, provided the dollar doesn't gain much more, still a lot cheaper than the UK.