Has Nigel Farage contributed to the downfall of four Prime Ministers?

Nigel Farage has led UKIP and then Reform UK, parties that have influenced Conservative Party strategy and voter shifts over multiple elections. Four individuals have served as Prime Minister since 2016: David Cameron, Theresa May, Boris Johnson and Liz Truss, followed by Rishi Sunak and Keir Starmer. Farage's campaigns on Brexit and immigration have been cited by some as factors in leadership pressures within the Conservative Party.