I've never rented a 3 bedroom so can't help there but you could look on www.slowtrav.com and check the vacation rental reviews. I've found them helpful in the past.

I can pass on some companies you could try but I think you want personal recommendations. Good luck, that sounds like a huge amount of money for a week so I hope you find something you like.

Kay

No personal experience (have only stayed in hotels and youth hostels in London), but if you want to consider decent looking properties in other areas here are a few I have bookmarked -

http://www.holidaylettings.co.uk/rentals/central-london-zone-1/150964

http://www.vrbo.com/323395

http://www.vrbo.com/360217

Thanks KayF and Farrermog

I'd maybe start w/ Farnum & Christ because they have some beautiful properties. Then on to vrbo

http://farnum-christ.com/

(the only 3 bdrm I've rented was a gorgeous 3bdrm/3 bath, two storey penthouse w/ 2 terraces that was w/i your budget but unfortunately it is no longer a holiday let )

thanks for the tip Janisj

We recently returned from our Europe trip and rented an apartment in South Kensignton (Rosary Gardens to be exact) from A Place Like Home. They were fabulous to deal with: great communication before our trip, returned our deposit a week after, and going above and beyond both when our plane was delayed plus over two hours in line at Passport Control on arrival, and accidentally locking ourselves out of the apt (and our luggage still in the apt) on check-out.

They manage a large number of properties - you can look at their website www.aplacelikehome.co.uk - and also email them your requirements and they can send you a list of available properties within your price range. Just a quick looks shows a number of properties fitting your requirements, such as http://www.aplacelikehome.co.uk/l197-cranley-mews-south-kensington-bqxeacpxf.aspx.

PS Meant to add that we rented a 2-bedroom, but they have a number of 3-nedrooms.

London Perfect has a number of larger apartments that may work for you.

www.londonperfect.com