It fraud…The last time I looked that was a criminal offence.
4 of you, you say…Report them to the police a criminal act has been committed.
It’s one thing for a worker to “take pseudo-PAYE on the chin” when performing work.
But, if the yard’s T&Cs include the ability to “charge whatever they like” to your pay, then they are admitting that THEY employ YOU, whilst regarding YOU as “self-employed” - which is completely bent on both accounts.
They rely on the fear and ignorance regarding tax laws - so the hapless worker does not complain, thinking that in any investigation - they are in as much trouble as the yard is.
Not true. The worst HMRC will do to a worker when reporting shennanigans such as this would be to bill you one week’s back taxes - which would likely be less than the £44 “fee” being recovered that was illegally deducted from your PAYE pay. If the pay was Self-employed “Contractual” - then surely it is NOT in the contract that you “consented” to the deduction of any fi fo fum fees that the ‘empoyer’ sees fit… They shoud be signing your contract/invoice - rather than dictate to you the other way around.
It isn’t in there now …Is it? 
Bill them. If they resist paying up, then they must supply such refusal in writing - which can then be used against them in a deeper HMRC investingation.
Telling HMRC of such things does not make you some kind of “grass” - you have merely reported a theft of money you thought was in your account. That’s not ‘false-accounting’ on your part.
In my last driving job before I packed it in I had to do the disclosure thing to get the security pass for East Midlands Airport, the letter did indeed come to my home address and I took it into work. It was done with Disclosure Scotamd.
Had to gave a CRB check for one of my current jobs, working in gyms, and that one didn’t come to the house.
I didn’t pay for either of them, the companies involved paid on both occasions.
name and shame please, even by PM if you prefer. This sounds like an outfit I’d like to avoid.