If you just mention that e.g. Tony Blair was prime minister of the UK at the time of your fictional events, then that is similar to stating that there is a city called London. It will be no problem at all.
If you describe Tony Blair doing what all prime ministers do (e.g. be friendly to a journalist) or what is a historical, documented, published and proven fact (and you mention this documentation and give your sources in an appendix), there will be no problem at all. Just make sure you quote the source correctly: if the source says "it might have been", you must describe the events with the same possibility of doubt.
But as soon as you have any real and existing person do anything in any kind of fictional work that either you have made up or that may be interpreted as reflecting negatively on that person, from picking his nose to starting a war, you will most certainly recieve a letter from that person's lawyer.
I would never do it. The newspapers are full of lawsuits for journalists mentioning the names of the children of celebrities, stating that a celebrity dyed their hair (German chancellor Gerhard Schröder sued a newspaper over this) and similar apparent banalities. I can't imagine the backlash you will face when you imply a politician might have lied to the public.
If the person is dead, go ahead, but as long as he is alive, make up an imaginary prime minster, just like American movies always have fake presidents in them.
If your whole idea hangs on working with something that everybody knows to be true but has never been legally proven, talk to a lawyer experienced in the relevant field (journalism, personal rights, rights over one's own image, slander, etc.) and pay for legal advice that you can rely on (and never trust anything written by anonymous persons on the web).