Here are a few options for you:
To organise your airport pick up by comparing the cheapest cab in London, please click here. You will be taken to a website that compares the price of taxis and will give you the cheapest quote. You can only do this for trips within 3 months. So if you want a quote but your are coming later in the year, just put in some pretend dates.
The address of your apartment for Comfy & Easy for Central London is…. 67B Waldemar Avenue, London, SW6 5LR
You could try Uber which is now operating in the UK, they offer a £15 discount if you type in this code signup15 Please click here if this interests you.
If you would like to use public transport please click here.