There are hundreds of interior designers in and around London, where to look is probably best determined by your budget, from there it is determined by your personal taste.
The Telegraph has a top 50 list of interior design websites which will help give you inspiration. (I am afraid the forum is not letting me post any links, if you search Top 50 Interior Design websites The Telegraph, it should come up)
If you like any of those designs it would be a good idea to follow up to the designer and see if they would be able to view your property.
Alternatively, by looking the designers up, most of them will have a portfolio of their work and you could decide on that whether they would suit your styles and tastes.
Alternatively if you do not mean someone to entirely dress your house, there are websites such as Roomservice by CORT (roomservicebycort . com) where you can rent furniture in pre-arranged sets. These are very popular for those renting or living over here temporarily (i.e. expats and such) as you can rent for up to 3 years, or if you decide to stay and you like the furniture, you can buy it from them and not change a thing!
I hope this helps (sorry about the links)
Ed