Oxford Street and Regent Street,
You can go into Selfridges for ALL different price ranges, and you have the massive flagship Topshop store there, that has vintage and limited collections instore.
Bond Street is amazing, but you will not find any reasonable priced items , Harrods and Harvey Nichols are in Knightsbridge, so a taxi ride away from Oxford/Regent Street.
Also consider Covent Garden, which has a fair few one off shops, as well as some well known high street names.
Have a great shopping day