“It doesn’t really make any difference who is Prime Minister.”

The claim is too strong as stated. In the contemporaneous Cabinet Manual (published in October 2011), the Prime Minister is described as the head of government and as being ultimately responsible for the policy and decisions of the government, with power over ministerial appointments and the overall organisation of the executive, so the office was not merely ceremonial. (cabinetoffice.gov.uk) A 2011 House of Commons evidence submission likewise said the Prime Minister had a powerful but contingent role and that the number of functions performed by Prime Ministers had increased, especially in policymaking. (publications.parliament.uk) And a later comparative study using UK data from 1980–2014 found that changes in governing party were associated with different policy agendas and reform intensity, which cuts against the idea that it makes no real difference who is in No. 10. (academic.oup.com) The evidence does support a narrower point that financial markets can be more sensitive to expected policy credibility than to party label alone, but it does not support the broad absolute claim that who is Prime Minister “doesn’t really make any difference.” Sources: Cabinet Office Cabinet Manual draft; House of Commons Political and Constitutional Reform Committee evidence on the role and powers of the Prime Minister; Trein & Maggetti, Policy & Society (Oxford Academic).