David Maddox: David Cameron and the G8 Summit WHEN the UK hosts big political events you can always guarantee an even bigger build-up. The run-up to this week's G8 summit in Northern Ireland has been no exception. But this time there has been a bit more of a frenetic urgency than might normally be expected, because while there are some weighty issues on the table the conference is also being overshadowed by speculation over Prime Minister David Cameron's political survival. Once the business gets underway, no doubt Mr Cameron and his ministers will want to walk away with some sort of agreement on Syria, a "get Google" accord on tax evasion and moves towards kickstarting the world economy. In themselves, all these issues are of great significance and delivering on them will be no mean feat. However, failure to deliver on anything, or much - and already the top priority of tax evasion is looking tricky - will underline the idea that Cameron is a weak prime minister, a view which, rightly or wrongly, many in his own party are increasingly coming to believe. With the numbers of Tory backbenchers writing to the chairman of the 1922 committee, calling for a vote on the leadership, edging closer towards the 46 required to trigger it, this summit could prove to be Cameron's last chance to show the doubters that he is a successful world leader who can deliver. Significantly, one of the speeches he made as part of the run-up to the summit was a direct attack on the eurosceptics in his party who want the UK out of the EU and are largely the people behind moves to force him out. Cameron wants to show that the UK is at its best when it is wielding influence as a member of one of these great international institutions and not sitting on its own on the fringes without any friends. But having promised his party that he can negotiate a better settlement on EU membership before taking it to a referendum, he now has to start showing he is capable of persuading international leaders to get what he wants. As difficult as the G8 agenda is to achieve, most people still think it is much easier that renegotiating EU membership, so little or no progress this week will reflect badly on his longer term aims and further undermine what faith there still is in him among Tory backbenchers. The good news for Cameron, though, is that he has already shown he can deliver. With the aid of the Germans, he managed to negotiate a cut in the EU's next budget, something most observers had believed to be an impossible task. Unfortunately for Cameron, even that was not good enough to put an end to the backbiting from backbenchers, although it did buy him time. Success this week will not end the speculation on Cameron's leadership but it will strengthen his position as the one Tory politician capable of delivering on the international stage. If that ensures he sees off a challenge this year then he should have a clear run at the 2015 election.