@McTag,
Thanks, McTag. I will certainly consider your advice. Actually I was asking because I was afraid that I could miss something interesting and never expected that somebody would know my personal tastes. I can hardly define my likes and dislikes; I like to see different cities on the whole, feeling them as living beings with all their history and modernity. London is special, maybe because it has pubs dating from XVII century. It does have its own soul.
My wife tends to make assessment on the basis of modernity and did not like New York and modern Paris and was fascinated by today's Berlin. I really wonder what she will say of London. I am more into history and only dislike Soviet industrial cities, which were quickly built on a grass field.
As to the fares, I think I will buy a week Travelcard. Is it possible to buy an Oyster card with a 7-days Travelcard that would only start the next day, and additionally top up the Oyster for a single passage from Heathrow to Hampstead?
Will try to keep you updated if I can. Unfortunately the first impression is already somewhat negative due to the new visa procedures. The first time the embassy simply asked about the purpose of my visit, the second time they wanted a salary certificate from my employer, now they also photographed me, took my fingerprints and their questionnaire included structure of my monthly living costs, date and place of birth of my parents as well as all those who was going to accompany me to the UK (fortunately I am not member of a big traveling team) etc. Next time they will probably ask for results of my medical tests. My fellow-workers tried to talk me out of taking this trip saying that the country is now unfriendly to visitors.