The current contract which sees the BBC and Sky "partnering" on F1 coverage runs until 2018.
In 2011 the BBC was looking at ditching F1 at the end of the then contract (2013) because of its obligation to make the budgetary cuts imposed by the Government back in 2010. ITV, Channel 4 nor Channel 5 had any interest in bidding for the upcoming broadcast rights meaning that no UK terrestrial channel would have shown F1 after that date. F1 would have moved exclusively to Sky.
BBC and Sky entered into this partnership for broadcast rights which allowed Sky full access 2 years earlier than would otherwise have been able, and the BBC to pay less but still show all races (half live, half as highlights) for many years after it would otherwise have disappeared off terrestrial TV. Without Sky this would have been the last season of F1 on BBC - now it exists until at least 2018.