Normally this would be handled by a wider synchronized network. The EU has a continent wide synchronized network and the UK isn’t part of it.
There are also other ways to store energy. For polar regions sand batteries are capable of storing heat for months. High grade heat to the point they can siphon off that heat for power generation.
The interconnectors between UK and the continent are HVDC.
As such they are essentially massive switching-mode PSUs, and there is no possibility of having a synchronised connection, as the AC has to be synthesised, following the local spinning iron.
But also europe isn't that large. When there is no wind in the UK, there is no wind in France or Italy. Which means not only do they not provide diversification, they will import at the same time.
There are also other ways to store energy. For polar regions sand batteries are capable of storing heat for months. High grade heat to the point they can siphon off that heat for power generation.