That "House of Commons elects the Cabinet" MPs in the house of commons elect the Prime Minister (typically this means the leader of the largest party). Technic

That "House of Commons elects the Cabinet" MPs in the house of commons elect the Prime Minister (typically this means the leader of the largest party). Technically it's the Queen appointing them, I believe on advice of the civil service on the basis that they will be able to command a vote of confidence, but in practice it's the MPs themselves. The Prime Minister then appoints the cabinet, most of whom will be elected MPs by their local constituents (in practice at least half of the seats in the UK are "safe seats", meaning the MP is appointed by local party memebrs) The Prime Minister also appoints one of the EU commissioners (and the PM's counterparts in the other EU states also appoint one). The EU parliament elects the president of the commission from a pool suggested by the heads of government. That president then allocates each of the commissioners they've been sent by governments to various roles.