I'd like to throw another lens into the mix. The
Tamron 70-300mm VC is £350 so it's more expensive than the 55-250mm but it's cheaper than the Canon 70-300mm. It's also much better than either.
I've seen back to back tests of the Canon 70-300mm and the Nikon 70-300mm VR and the Nikon wins hands down on image quality. However, the Nikon was compared to the Tamron in AP magazine a few months ago and it won that so it's leagues in front of the rather old (by comparison) Canon 70-300mm.
The 55-250mm isn't bad optically and it's fair to say it can outperform a few others. It's build quality leaves something to be desired though.
The Canon 70-300mm is not worth the consideration really. It's got a micro USM motor (rather than the preferable ring USM), it extends and rotates on focusing and it's optically a relatively old design.
More than anything this comes down to budget, but it's a no brainer for me. Less than £300 and it's the 55-250mm. Less than £350 and it's the Tamron by a mile.