have a look at the maximum loan amounts then deduct his accomadation costs. The amount left is the minimum you should top up by.
Exactly that. Maximum maintenance loan outside London is £8430 for 17/18. All fairly clear cut at this point.
However as others have pointed out costs do vary thereafter.
DS1 is at the better value end. Accommodation for 17/18 just over £4k. That would leave around £4200 to top up, so in his situation, works out to bang on £150 per week for everything else including food. Does he need that much? Does he spend that much? Honestly don't know. With well paid vacation employment he's probably not going to struggle financially and if he is building on his savings for life post Uni all well and good.
Had he gone to his insurance choice, and assuming in hall, he'd be looking at just over 7K accommodation cost (catered, not en-suite but with meals paid for whether he turns up and eats them or not). So suddenly, using the maximum loan as a guide again, around £1300 tops up that, or around £42 per week. For completeness the self catered option would still be just over £5k, so if topped up providing around £100 per week.
Uni choice does have a massive impact, and I fear more Unis, certainly at the higher tariff end, seem to lean more towards more expensive accommodation.