Thing is, paddyann , they don't actually rule. They are figureheads with no influence on government policies, and their allotted task is to charm the representatives of other countries and to have the experiences of many years of meetings with previous Prime Ministers behind them to relate to current PMs and possibly impart some general (and non-party) advice. HM has met, worked with and formed personal impressions of PMs from Winston Churchill to Theresa May, and she reads up on the contents of her red boxes. She has more experience of the ins and outs of goernment than any sitting MP.
Presidents in the US mould do expect to influence the government of the day. They are strongly mono-party, becaus they owe their position to being voted in on a party ticket, and some are hell-bent on destroying the achievements of their predecessor.