Hi, Bougainvillea is a genus of 14 species, most of which are frost tender, but there are 3 that can withstand temperatures down to zero for short periods, but they will start to drop leaves, plus they have to be kept fairly dry, they're not really a plant suitable for the U K , because they don't do well in pots, which you would need to take into a greenhouse in winter, plus if you had them in pots, you wouldn't get the effect of the trailing flowers, I've often wished that the U K was warm enough to grow these as nature intended, but our climate, {as yet}dictates that we can't, and if these have been left outside all winter, they will have been more susceptible to cold, by being in pots.
But, if you want to know if they're still alive, scrape a little piece of the bark with your thumbnail in a few places, if the underneath is brown, it's dead, if it's still green, then it's still alive {just}, personally I wouldn't hold out much hope.
By the way, the pot which is wider at the shoulder than at the neck, would give you great difficulty when the time came to repot, as it would be full of roots lower than the neck, although they look very nice they're not really practical, Derek.

Give it the scratch test. Scratch away a little bark; Green=Alive, Brown=Dead. You should see some evidence of growth by now.

Thankyou for your help. One of them is brown the other is green. I really hope it grows and flowers this year. I will post a photo if it does. We will take your advice and repot Derekm, you never know it may help.

The soil looks pretty dry, too. I know that Bougainvilleas have the reputation of being drought loving, but that is only in the ground, where they can grow deep roots. In pots, they need just as much water as any tropical plant--less than ferns, but much more than succulents. They also need regular feeding with something like tomorite.