It is an extremely bad idea to make MPs' staff direct employees of the House of Commons.
There are all sorts of reasons for this, but not the least is that such jobs would then effectively be restricted to people straight out of the super-posh universities to which they had been sent by their super-posh schools (by no means necessarily private, at least officially).
This is already very largely the case. But it is still possible for an individual MP to make exceptions. For anything like the foreseeable future, the House as an institution would never do so.