There is no need for Mr. Blair (or any other prime minister) to have his own plane. He is a private citizen like anyone else in the UK. The Queen is the Head of State in the UK (and therefore the equivalent in the UK of the President of the USA or any other republic) and therefore gets (or got) the "state" plane, palaces etc and carries out all the duties of Head of State that in the US are carried out by the President.