There is currently a 2GW connector to France, I believe.
I have no information on their contractual obligations, as even France may not be keen to export electricity on a cold winter's day - has anyone better information?
On a brighter note, these prices for gas should make nuclear costs unchallengibly competitive, in spite of rising construction costs.
Of course, the British government has done everything possible to make it difficult to get started on a nuclear revival, as they have turned down a bid for the nuclear sites from EDF, who could undoubtedly have done the job, and now propose to have different consortium;s building at different locations, with all the waste and delay inherent in that approach.
The record time for a build is around 4 years, in the far East - it looks like our establishment intend to add a nought to that.

Chris Vernon's post downthread gives information on 'The French Connection', which shows that it is indeed 2GW, and further shows its availability during a cold winters day - for much of the time is it not available, although it does kick in again at the top peak.
In practise it may be easier to get France to build some more capacity for export near to the channel whilst we await action from our Third-World class government to order and build capacity, not to mention their ability to run them properly.
Four modern Areva twin reactor set-ups would provide around 12GW of power to the grid, and they could be built in perhaps 6 or 7 years - that would, incidentally, be more than the average hourly power projected to come from the off-shore wind build, at a fraction of the cost and a lot faster.