What are the limits to the PM’s power?

The PM must maintain the support of their party; if the party turns against the prime minister then they will lose a great deal of power and possibly could lose office.
Margaret Thatcher lost the support of the Conservatives in 1989 for the unpopular poll tax and senior minister Geoffrey owe resigned over disagreement with her euro sceptic views – she was voted out of office by her MPs.
May resigned in 2019 after the leaders of 70 Conservative Associations signed a petition calling for a vote of no confidence.

PM’s strength depends on the size of their parliamentary majority, if it is small, they may struggle to retain the support of Parliament.
John Major lost his large majority after the 1992 election and so lost authority.
May became reliant on the DUP after the 2017 Election which resulted in a hung parliament.

Occasionally the prime minister may be confronted by a united cabinet opposition and will have to back down. Tony Blair hoped to bring Britain to the European single currency, but most cabinet members insisted that it should be delayed.
more of a problem in coalition gov – Cameron 2010-15 – had to apt 5 LD ministers.