John, many are having this problem in the cold weather.
However it’s not too frosty anymore and yes to move onions, lettuce etc to a tunnel, even to plant them if large enough, with fleece over.
But the warmth loving plants you mention will be retarded by cold nights in a polytunnel, even fleeced.
On the other hand in sunny Exmouth by the Sea you may get away with it. Not the cucurbits though, I have not even sown them yet, no rush this year.
