Is the Prime Minister Effectively a President?

Arguments that the UK PM is now effectively a president include:

The media concentrate more on the PM as government spokesperson
The greater concentration on presentation of policy
The greater importance of the ‘presidential’ role in terms of foreign policy, military issues, global conferences and so on
The growth of the Downing Street ‘machine’, looking increasingly like an ‘executive office of the president’
Spatial leadership issues- the PM developing a personal policy agenda, separate from their parties
The increased use of special advisers personally loyal to the PM
The personality of some prime ministers, notably Blair, Cameron

Arguments that the UK PM is not effectively a president include:

Prime ministers are not heads of state constitutionally
They are limited by party, cabinet and parliament- it is much easier for them to be removed than it is for a president
PMs can be removed from office in mid-term, for example Thatcher
It is very much an issue of the individual’s ‘style’- the PM may act like a president, but that does not make them one constitutionally
Events and other factors cause variations in dominance- certain PMs may be more presidential than others

What is the idea that government as a whole is responsible to Parliament?: Collective Responsibility
Who resigned over planned cuts to disability benefits in 2016?: Iain Duncan Smith
Which event in 2008 damaged Gordon Brown’s reputation and authority?: Financial Crisis
In 2016, why was collective responsibility relaxed?: EU Referendum
What is the biased or one-sided presentation of information?: Spin
What is an informal group of advisers consulted by the PM?: Kitchen Cabinet
Which powers were once held by the monarch but are now used by the executive?: Royal Prerogative
Which Prime Minister effectively resigned due to the lack of support from their cabinet?: Thatcher
What is the ability to make appointments?: Patronage
Which Prime Minister’s power was restricted by being in a coalition?: David Cameron