Mustang wrote:

What about digging it up and storing it somewhere? In the US, some dig
their nanas up and store them somewhere dry, cool and dark, such as in
a cellar or even under the house. Then, next spring, they pop them back
in the ground.

This is done because of the intensity of winter cold. The ground often
freezes solid to a fair depth in states where they are dug, which can
kill the rhizomes. The return of serious heat in spring enables even
the most weakened root-stocks to make a very fast and full recovery.
By contrast in the UK, springs are often long, cool and usually wet
only warming slowly over several months. If the roots are to be dug
and then replanted each year, they need to be restarted under glass
(preferably heated) to get the plants moving quickly.

Basjoo is root-hardy in most areas of the UK., especially if mulched in
the southern counties so there's no advantage in digging it up. The
set-back caused by root disturbance is unnecessary. The point of
protecting basjoo in the UK is to try and prevent the pseudo-stems from
dying down to the ground, so that the clumps can become very tall and
impressive and may even flower. If you are growing Musas or Ensetes
that are more tender and cannot withstand winters outside, then you
have to lift them or resort to very intensive insulation methods.
However, I would never disturb a plant unless it was vital for its
survival.