I have used a chauffeur service for work where the driver does private jobs. It costs £50 to/from Cananry Wharf (where I live), and may be slightly less for the West End.

The driver uses a blue merc and keeps it in immaculate condition and usually for my pick up is early and has always been there on my return to Heathrow, even with 5.30 am landings.

If you want his mobile, let me know.

Cheers