We are staying with friends in Cheltenham, looking for 1 -3 day tour (preferably guided) of London.
Can't really help you with that one. How much longer will you be there? If you have several weeks you could pick up a Gloucestershire Echo (paper) and look through for coach trips to London. Usually they are printed several weeks prior to the trip, and the coach will usually stop at various collection points in both Cheltenham and the surrounding towns.on the way.
The coach will usually be mostly pensioners.
The trips normally are in conjunction with the visit to Windsor Castle or a West End show, usually with one overnight in a cheap hotel.
I don't know of any which are guided tours but when you look through the paper and find these ads you could ring up the companies and ask for details of any they would know guided.
doubt there will be much demand for this - just take the train to London and find a tour there if you that's what you want