Most schools in the UK are academies now.
Maintained schools can use unqualified teachers via 'back door' methods.
They can hire unqualified teachers if they commit to training them.
They can also use HLTAs to teach classes within specific parameters. Unfortunately these parameters are fairly loose and ambiguously worded so schools can quite easily make a legal case for using a HLTA to cover a lack of teaching staff.
Therefore, in this case, a HLTA being directed to teach a class but not having sole responsibility for them is perfectly legal in a maintained school as well as an academy school as long as it's for the 'short term'. 'Short term', however, is not legally defined. There is union guidance but not a legal definition.
Is it good practice and is it ideal? Probably not.
Is it better than have a stream of supply teachers? I'd say so.
Is it fair on the HLTA? No. They're being paid much less than the classroom teacher would be, to do pretty much the same amount of work. But at the same time, they don't have to say yes to the job.
The reality is, schools can't get enough staff, and if they do have enough staff, they can't afford to pay them properly. It's a dire situation. And yet no one is really advocating for proper change. Teachers are still viewed as a bunch of whingers and criticised every time we go on strike for inconveniencing parents. Without parental support, we won't be able to get the better conditions needed to retain staff and ensure a qualified and experienced professional is teaching your kids.