I have a friend in England ready to welcome me for a short holiday. Where or which office should he approach with his invitation for my visa application?
None. Your friend doesn't apply for a visa for you, you do. This letter will be one piece of documentation you need, you will also need to prove ties to your country and so forth. For example, this is the site to check for if you are in India, this is Saudi Arabia and so on.
In general, in almost all cases it is you who apply for the visa. There are a few work visas where the employer applies but both for visits and immigration, the fundamental rule is the visitor/immigrant files with the optional help from some entities in the target country.