@Angharad01 as a veteran of Cambridge rejections I feel your pain! DS1 was like a lost soul after he was rejected first time, then in real shock when he was rejected second time as he had a super high BMAT and achieved grades. He just did really badly in Cambridge interviews because he cared too much. After a couple of weeks he focussed on his other choices, when he did not get any offers he was very down. I told him it gave him an opportunity to have another go at Cambridge, tried to stay positive. Now, as a second year at St Andrews, he is really happy there, feels the workload is intense enough and is glad he doesn't have to do an essay every week!
Apart from the elements of other courses which many people prefer outside Oxbridge, there is also the issue that your F1/F2 options depend on your placing within your cohort, so if he is a bigger fish in a smaller pond he may get a better ranking. As mentioned above, this is an unlucky year, when Cambridge publish their stats I expect you will see another drop in the number of offers due to current grade inflation. Not all colleges have lovely accommodation - my niece at Christ's didn't have en suites, so if he had been picked out of the pool, he could not have counted on that!
If he meets their widening participation criteria (non selective state school and postcode) he maybe have another opportunity in Adjustment.
Re Further maths, do you know that everyone is entitled to 3 years of sixth form? DS2 did the wrong A levels, no Chem or Bio, so he could only apply to Manchester with a foundation year and Newcastle this year. If he doesn't get an offer he is staying in at school for a Y14 to do Chemistry. Our school teaches FM in a year anyway - if you do double maths you do normal A level syllabus in Y12, FM in Y13, so it is not a problem doing FM in a year and it doesn't have to be alone. The admissions tests - MAT for Oxford is taken at the same time as BMAT, STEP for Cambridge is an offer condition and is taken at the end of June. Both are super hard.
I would advise you to let him know you will support him in whatever he wants to do, but that there is no hurry and it would be great to do his best to get offers to keep his options open and prove to himself that he can get offers.
Good luck!