No, Bears extinct in Britain for at least 1100 years and possibly longer. There are writings from the Roman Empire (eg Martial in 81AD) which state that bears from Scotland were preferred for the spectacles in the Collosseum in Rome, but they were definitely extinct
by the 10th century .
However, there are bears in zoos, to say nothing of Paddington, Winnie the Pooh, Rupert and the bears that will eat you if you tread on the gaps in the pavement(sidewalk).
It's always worth knowing what to do with one if you find it in the garden especially if polar bears really are moving south in search of food.
On a more serious side there are people who are keen on reintroducing wolves and wild boar to Britain so it can't be long before someone decides bears would be a good idea.