Particularly if you are staying a week, or have children and need space, apartment rental can be a good option. A typical place works out slightly bigger than a hotel of similar price, and gives you the option of saving on bills by cooking yourself. On the minus side, you usually have to clean the place yourself, and eating out is one of the reasons to come to London, whilst shopping for food is a time consuming chore.
Citadine is a large global chain that has places in several locations throughout London – in Gloucester Road, Trafalgar Square, Holborn and Barbican. They offer studio flats, with a kitchen and usually with a sofa bed. Rates are around £90-110 per night for a studio flat suitable for 2 people, to £140-170 for an apartment suitable for four. Rates are cheaper if you stay 7 nights or more. A related group, the Ascott group, owns two further places in Mayfair and Bayswater.
Coach House London Vacation Rentals have a range of places available through out the city from around £100 per night up; they specialise in private houses where the owners are temporarily absent.
Regent Suites is a US based site with a good selection of London properties, quoted in US$.
Mayflower apartments, linked to the Mayflower hotel, in Earls Court, have one bed apartments from £95-170.
JSK apartments have a range of places throughout the UK with a reasonable selection in London.
London House offers cheaper, modern looking apartments in a block in the Bayswater area, from around £70 per double.
Shortstay London has a range of places that are let out by the week (from around £1000 per week). Their website is very good for giving information and pictures about each property.