Will paying off SL that's on a DD mprove affordability or is better to have a higher deposit for hou

RD88

My partner is due to pay off his plan 1 student loan in 17 months. We're also looking at applying for a mortgage this summer. We decided to get his SL on a Direct debit, mainly to reduce the chance of an overpayment at the end, but also be because we thought it might be better to no longer have it on his payslip when being assessed for mortgage affordability. It may make no difference but we at least have a letter from SLC with the start and end dates of the DD and the amount. 

Question now is that we have enough savings to clear the 8k owed on it. As interest rates on it are likely to stay above 5% for the remainder of it's life and we can't get an equivalent or better savings rate normally we'd get right on and just clear this. Except we'd be reducing the cash we're putting down on our next home. Is this worth doing? is it likely to improve affordability so that we can borrow more? or is it better to keep the higher deposit. His repayments are £500 a month so it certainly will benefit our disposable income overall, but unsure if in the short term there's any reason so do this prior to being assessed for a mortgage. 

I also have a SL but am only repaying 219 a month and still have around 15k on it, I don't expect to clear it for some time and would be reluctant to pay off should BoE rate come down again. His is more straightforward as we know it won't for the remaining term.