You can enjoy the lush foliage of the bananas in the UK by growing Musa basjoo. It can make it through a UK winter unprotected if you're lucky and the weather is mild, however it is an expensive plant so it's worth making an effort to protect it. When Which? Gardening magazine trialled different methods of overwintering Musa basjoo, the following method worked best for us:

Caption: Musa basjoo adds a touch of the tropics to UK gardens

Wrapping Musa basjoo

The best method was to wrap the plants. We started by cutting the plants down to knee height. We then erected a ring of chicken wire, supported by stakes, around each plant, into which we packed loose straw. We then topped the lot with a sheet of plastic to keep the rain off.
When we unwrapped the bananas in May we were doubtful about how the plants would have fared. They were yellow and sickly looking, but within a few weeks they had perked up and a huddle of new shoots were pushing up around the old stems.

Other method we tried:

Lifting and overwintering Musa basjoo in a greenhouse

Lifting and overwintering in a greenhouse worked far better, and the plants quickly grew from around 100cm to 180cm when planted out in late spring. However, lifting them and replanting was hard, heavy work and they looked very sorry for themselves in the greenhouse over the winter, with yellowing, droopy leaves.