What are the requirements to be in the House of Commons of the United Kingdom?

I take what you mean by 'be in the House of Commons' is be a Member of Parliament, representing one of the constituencies in the UK.

In order to become an MP, you must win the most votes when 'standing' in a constituency at a General Election, or alternatively when the current Member of a constituency dies and a by-election takes place in that constituency.

Currently, the UK runs a First Past the Post electoral system, by which the Member who receives the most votes in a constituency election, regardless of percentages, is given the Seat (represents them in the House of Commons).

If you stand as a Member belonging to a political party, then you must be selected within that Party to stand for constituency election.

In all cases, a deposit of £500 must be paid to the electoral authorities, returned if the candidate receives over 5% of votes at the election.

In short, the only requirements to become a Member of Parliament is a £500 deposit and the winning of the most votes in a constituency election.