"Have they quantified and identified it" - no; or at least not according to the NUS as quoted above.
There is no evidence for an increase in prostitution amongst students. Indeed there may also be an absence of baseline data, so it would also be impossible to demonstrate an increase, especially as reporting from earlier years and other countries shows this is not a phenomenon linked to the timings of the change of administration or the roll put of any particular policy.
And I'd like to ask again, how do male students (equally impoverished) cope? Unless the NUS is equally concerned about a rise in dubious employment amongst men, then it does seem that alternatives exist.