is the prime minister a member of the house of commons
Although it does not formally elect the prime minister, the position of the parties in the House of Commons is of overriding importance. By convention, the prime minister is answerable to, and must maintain the support of, the House of Commons. Thus, whenever the office of prime minister falls vacant, the Sovereign appoints the person who has the support of the House, or who is most likely to command the support of the House--normally the leader of the largest party in the Commons, while the leader of the second-largest party becomes the Leader of the Opposition. Since 1963, by convention, the prime minister is always a member of the House of Commons, rather than the House of Lords.
House of Commons of the United Kingdom