OK, just to answer some of the questions and ideas people have suggested.
I did initially think about running the cable across the houses somewhere near the soffits, and then down to the garage. No one else in my terrace has power to their garages (They only use them for storage), but I'm pretty sure they would be fine with it either way, they are all very easy going, and we get on well with them. Obviously if I was to attached anything to their property I think I would definatley get this agreement down in writing. Just in case.
The idea of 12V car battery with 12V lighting is fine, but im unsure as to how long that would power for, and ideally I would prefer a more "permanent" solution.
Solar is a very nice idea (and I like the green side of it) but its still going to cost a fair whack to install, (and if it costs the same as a wired solution, welll then my "greeness" will go out the window!)
Again 12V Car starter is an idea, but how long is that likely to be able to provide power for?
I think my next step will be to get a few electricians out and see what the quotes are. That way I will be able to decide if its something I can go for.
Out of curiosity, is there a way to hook up some flourescent lighting and be able to just plug them in to a socket (if i was using an extension cable from the house?