Try the charity shops in smart affluent areas. Primark, Matalan & TK Maxx also often have reasonable bags. Apparently there is a website to rent designer handbags but that would cost you at least £20 and you'd have to give it back. Google 'Handbag Rentals' for a list.
Have a look on ASOS (As Seen on Screen). They do accessories and clothes based on what the celebs are wearing - e.g. Sunglasses in the style of Paris Hilton. You can get a bag which looks designer but isn't - but to be fair, they do range in price from cheap to real designer stuff which are super expensive....but it's always worth a look, I have had some great stuff on their without a massive cost!