The Prime Minister and Michael Martin, Speaker of the House of Commons, are also lending their support to the competition for schools being run to mark the bicentenary of the parliamentary press gallery.
The 24 finalists will spend a day at the House of Commons in February. They will meet Tony Blair in Downing Street and will be given a tour of the Speaker's rooms by Mr Martin.
Mr Blair believes teenagers have much to gain from the competition. He said: "Young people can make a real difference in politics, if they know how."
And Catherine MacLeod, competition organiser and political editor of the Glasgow-based Herald, believes involving pupils is vital at a time when politics can seem riven with internal turmoil.
She said: "The political class has left a lot of non-political people behind. But if young people understand the political processes better, they will be more inclined to vote."
The competition is being staged by the parliamentary press gallery, which was set up 200 years ago to guarantee the right of reporters to work in the House of Commons. It is supported by The TES.
Students between the ages of 16 and 19 have been asked to submit an essay examining elements of parliamentary politics. Almost 200 entries have been received so far.
The deadline has been extended by a month, to December 4, to allow Scottish students to compile entries during their half-term. The judges have also decided to accept entries in Welsh and Gaelic.