Surely, if you have a student ATC license you stand in better stead than somebody with a few A-levels in P.E?
That would rather depend on your explanation for only having a student licence as opposed to a full validated ATCO licence with least one rating, then convincing the interview board that they should spend upward of £50k on your training when you may have already failed once.
The competition for this particular post will be bright young things, bristling with good, solid academic qualifications with high pass marks and there'll be stacks of them.
I strongly suspect that Southend, (in line with a lot of other similar airports taking on ATSAs for future ATCO training), are seeking someone willing to learn every aspect of ATC at a regional airport who will be ready for ATCO training as part of the unit plan to replace retiring ATCOs.
As HD said, employers can demand whatever qualifications they feel appropriate these days. Having a student ATCO licence is one thing, but it pails into significance compared to a good all round education with good academic exam results.