How old are you? Do you mind hostels?
Hotels are hella expensive in London. I stayed in one once that emphasized luxury and it was...in the lobby. My room was smaller than my closet at home.
When I last went in '06, the hostel I stayed in in Hammersmith was 5 minutes walking from an underground station, my room (a private one with 3 friends) was huge, the kitchen was enormous. Depending on your GF, though, because most girls I know won't enjoy shared bathrooms. If you're outgoing sorts of people, you might meet some other cool travellers.
You might even meet James May like I did.
In Paris, try to stay away from the Northern end of the city, which is the ghetto.