Hi - I assume your student loan is here in the UK?
If so - no, it does not make sense to pay this down first.
Generally speaking, I agree it makes sense to pay down debt before investing / saving an emergency fund, particularly if the level of interest is greater than that which your investments will likely earn.
However, due to the way UK student loans are structured with debt forgiveness and only paying back once you've exceeded a certain income - it doesn't make sense to pay it back aggressively as you may be repaying a loan you ultimately don't need to repay. I think of UK student loans as a 'graduate tax' I pay on my income, rather than as a true debt which Martin Lewin (Money Saving Expert) also advises.
I wrote on this topic here: https://theprogressionplaybook.com/university-degree-pointless-or-an-essential-step-in-your-career/30
MSE have the same guidance here: https://www.moneysavingexpert.com/students/student-loans-repay/61