Heya - I used to live in London and whoever told you that you can't buy classics books there is worryingly ill-informed.
You can get the full price, expensive sort from Foyles, in Charing Cross Road, but the best place is the Hellenic Bookshop, on Fortress Road, in Chalk Farm (just past Camden on the Northern Line). Get out of the station, take a right and then another right, and keep heading up the road. It'll be on your left, and has pretty much any classical book you might need, all second hand and fairly cheap
The best place to look is downstairs, but it's a bit jumbled.
If you do come up to Oxford at some point, there are millions of classics shops here, and it's always worth a stop at the Classics Bookshop on Turl Street.
In terms of the best edition - the Loeb has a facing translation which you might find useful but is a bit outdated. The Oxford Classical Text is a more definitive version but doesn't have a translation or notes. The Cambridge editions are normally good for commentaries, in english rather than the OCT latin
If you're reading any Homer, btw, it's always worth picking up a copy of the Homeric Dictionary, which is probably available on this site, but I'm not sure. Again, the Hellenic Bookshop should have it