Good luck in finding something suitable!
My son had a hell of a job getting a work experience placement. Most places said it would cost them too much to take out insurance etc. Others had contracts with Stafford College to give the placements to them .
In the end I got him placements in Barnfields school ,(because the teachers knew both him and through me working there) and the Nelson Library in Staffordshire Uni (which has now gone, so no point asking them for a reference..). The Uni library had a website where you could apply, the same as the NHS . But If my memory is correct, you needed to be 18 or over to get a placement in the NHS at that time.
Then came the problem of finding voluntary community work when he started 6th form...same thing again, it would cost them too much for insurance etc etc
Ended up doing a few hours in the local playgroup, again because he went there pre-school and I knew the boss!
I think if schools require students to find work placements, they should at least have a list of firms willing to take them on .