The King would be the figurehead you’re thinking of. The PM may seem at the behest of his MPs (or the MPs of parliament in general), but, as we saw with Boris (fucking) Johnson and David (oink) Cameron, they can whip MPs, expel them if they defy the whip, prorogue parliament, call referenda, and many other acts which allow them to do as they wish if they wield their power in the ‘right’ way. There are things which the PM can do outside of parliament, as with any leader of a country; this includes starting wars, appointing members of the cabinet (and other branches).