London is a bad idea if he wants to save money unless you live in London (not possible to get trains home out of London much after 11pm).
As other have said - full time Oxford undergraduates have to live within six miles of Carfax tower - at the bottom end of Cornmarket Street, during term time. Even postgraduate students have to live with 25 miles of it.
I went to Oxford. My back up choice was Reading which was commutable from where I then lived - that's now 25 or so years ago.
Don't pressure. Do talk through the finances. Oxford has some bursary funds in addition to standard student finance. He needs to look at the financial situation with the other unis.
Oxford doesn't allow students to work during term time (some occasional rare exceptions for the odd couple of hours but nothing like a standard part time student job). But has longer vacations.
If Cambridge offers the better course and he's been to open days at both Oxford and Cambridge then he may as well go for the course he really wants to do (understanding it'll be more difficult for you to come over for lunch / to watch a play etc).
Saying that I picked Oxford over Cambridge for being about an hour away from home. I only went home in term time overnight once in the three years.
Having a back up option with a lower UCAS tariff that's commutable from home is a good contingency plan at this stage (don't know the dates nowadays for when you have to accept offers). It's a different uni experience but has particular advantages if A levels don't go to plan eg. keeping any Saturday job while studying / less debt / local knowledge re finding other part time jobs.
Warwick was a really good place when I looked at it 25 years ago. I'd pick it over London.
For other keeping costs down strategies I'd look north for cheaper accommodation.
For commuting to uni, think about public transport/ car parking facilities/ taxis and also look at things like youth hostels / Travelodges etc - he will need either a way to get home late at night sometimes and for that to be ok with everyone else in the house and / or sufficient funds he can stay over somewhere local to uni after nights out. Obviously he can't drive drunk. An hour's commute each way is probably too much especially for subjects with lots of contact hours. Are there any suitable unis within about 30 mins commuting time?
If he's going to live with you and commute to uni there will probably have to be a lot of adjustments to how you interact day to day - you're not going to know where he is / what he's doing / when he might be back beyond whether or not you're cooking for him. He may want to bring casual partners home.
If he's motivated to study and actively wants to save money by living at home you'll be able to make it work. Otherwise providing the finances can be made to work he's going to be better going and living at uni.