Work around here is very stop start at present. One week it’s mad, 50+hours, and another week it’s dead with queues getting a single shift at the supermarkets. 
Over a month, you might find yourself working:-
Week 1: 52 hours
Week 2: Zero
Week 3: Zero
Week 4: 54 hours
As PAYE, it looks like there’s an opportunity here to have it belt and braces…
I’ve heard it said that “You can’t get Tax credits AND JSA” - but the criteria HMRC keep telling me for getting tax credits is
“An average 16+hours per week over a rolling 4 week period” - which the above scores “average 26.5 hours” for. 
This average (in the example above) even looks fine following the mark-up in April from HMRC’s expectations of “16 hours” rising to “24 hours” per rolling week average to continue to qualify for tax credits from then. 
The big question is, do you sign on for the two weeks in the middle?
You’re not having Tax Credits stopped after all, and your still likely to be grossing over £1k a month. I think JSA recipients get Free School Dinners & Council Tax paid as well, but not their mortgages paid. 
The thought of a total monthly net income exceeding a grand for only working 10 days a month certainly has some appeal to it… 