For it will be the job of a man widely regarded as a cabinet Eurosceptic to guide Britain successfully through a referendum on joining the single currency, if the government decides that its five economic tests have been met. be.
Jack Straw's C.V.
But others see it as the first step to doing just that, arguing that it will be easier to swing opinion if a converted sceptic is at the helm rather than the openly Europhile Mr Cook.
Whatever the strategy in Downing Street, there is no doubt Mr Straw is a highly capable performer who is trusted by the prime minister and seen as a safe pair of hands.
As home secretary for the past four years, he rigorously pursued the government's aim of being "tough on crime and tough on the causes of crime".
To satirists and the left he appeared to be trying to outdo his Tory predecessors with his tough line on asylum, teenage thugs and curbing the right to trial by jury for some defendants.
Mr Straw's toughest moments came after his decision not to extradite the former Chilean dictator, General Augusto Pinochet, to Spain to face charges of torture and violation of human rights, but instead to allow him to return home on grounds of health.
For the man regularly seen as one of the most right-wing in the government, Mr Straw comes from a left-wing family, though he was sent to the private Brentwood school in Essex.
His great grandfather took part in the battle against removal of common land from villagers; his grandfather was a Labour activist, his father was a conscientious objector and his mother was also a socialist and pacifist.
At the age of 14 he joined the Labour party and by 1969, with a law degree from Leeds University behind him, he became the left-wing leader of the National Union of Students at the height of radical unrest on Britain's campuses.
In 1974 the then-social services secretary Barbara Castle took him on as an adviser and he inherited her Blackburn parliamentary seat in 1979.
Mr Straw rapidly moved into the Neil Kinnock camp and later, through the long years of opposition in the 1980s and 1990s, completed his journey to the right - spending three years as a Blairite shadow home secretary.
On taking the real job with Labour's first landslide in 1997, he was soon being attacked by the left as illiberal for his zero tolerance of "winos, addicts and squeegee merchants".
But after his own brush with youth crime, when it was revealed his 17-year old son had sold cannabis to a newspaper reporter, he gained great public sympathy.
He took his son to the police station to face up to his crime and was painted as a typical father trying to do the best for his child.
Mr Straw will barely have time to settle into his two official residences (Carlton Gardens in London and Chevening in Kent) before he will be off to the EU Council in Gothenburg, Sweden next week.
There he will hope to meet the guest of honour George W Bush to try to cement the "special relationship" which is in danger of becoming strained over plans for a European Rapid Reaction Force, which some believe could undermine Nato.
But it will be the way he handles the challenges of Europe itself over the coming parliament by which Mr Straw's success or failure in his new job will be judged.