There are few countries in the whole world where the tea and the tradition of drinking tea are important parts from their history. One of these countries is England itself and the practice of afternoon tea is dating from 18 century and the seventh Duchess of Bedford Anna who instructed all her servants to bring her every afternoon tea with little cakes. Very soon this custom become very popular and took place in each part of the social life and entertainment. In the past a lot of tea gardens were opened all over the UK.
Now days this tradition is saved and continue its existence in the hundreds tea shops, restaurants of the 5 starts hotels, typical English houses turned into attractions for tourists etc. During the centuries the tea turned into essential part from the English life style and the perfect time to have it is just between the light afternoon meal and the dinner. Also refusing to accept the invitation of an English man for an afternoon tea could be consider as an insult and disregarding of the traditions.
So going to England and not having a traditional tea is like entering the candy shop and not taking a candy. Planing a holiday trip to London is not much time consuming may be it will be more difficult for you to select the stay place. There are few options you may choosing from hotel, hostels or some of the cheap holiday apartments in London. To feel the real spirit of the country and the city it will be better if you just take a local rental you will certainly feel yourself at home even though you are in a different country.