Eye-opener tours at the British Museum are free 30-40 minute introduction guides that are done throughout the day from 11:00am - 4pm. Each one covers a different geographic area or topic. You can't do them all in a day simply because the tours overlap from a timing standpoint and they also start at different places in the museum.; sometimes the tours are in adjoining rooms, other times at opposite ends of the museum.

If you are looking for a quality car service, the standard in London is 'Addison Lee'. They are THE mini cab company.
You need to pre book, all possible from their website.
They have two types of car service - regular and executive. Regular being a mid ranged car, executive being a Mercedes. They will cost around £60-£85. Drivers are wonderful people, well dressed, will look after your luggage etc.
If you want a great arrival, an efficient collection and a high service mindset go with them. Save your use of a black cab when you are in the city dashing here and there.

Hi
My 82 year old mother and I used Heathrow Shuttles (www.heathrowshuttle.com) for our trips to and from Heathrow Airport earlier this year. They provide a door to door service and I see on their website that your hotel is on their list - should be about GBP28 for the two of you, one way. We found the drivers friendly and very helpful with our luggage. You can book on line. After a long flight it was great not to have to worry about changing transport modes and negotiating stairs with our bags.