Bristol is a very good option and has good career outcomes including lots in finance if that is what he is targeting. Its very good for the social side as well.
If he applies again it will be on basis of actual grades achieved rather than predicted so firstly I would see what he gets. The trouble is predicted grades are often raised by one grade and I think they are counted equal to achieved grades so if he does go down from 3 A stars it would add to risk. So would wait for results before a final decision.
Of the E&M students DD knows all had Bristol or Bath as their insurance and all got rejected by the LSE (about 40 she knew/questioned). Though in her year there was no TMUA for LSE and I think the issue is for LSE you have to declare if you are sitting TSA so they know you are applying to Oxford. The LSE used to rely heavily on personal statement and wanted a strong commitment to a maths based course and LSE I would guess so by having a different course they don't like it. How much difference TMUA would make I don't know, I would not put Oxford or any non very maths heavy course in if targeting LSE. I have heard of people getting Cambridge and LSE offers and those are both heavy maths based courses so similar. Basically stick to similar courses.
If your DSs school is a big sixth form or very good at admissions worth asking them success rates to give an idea of your odds. With Economics you get all A star students with strong super curriculars and many with FM who get rejected from very competitive courses with no obvious reason for rejections other than volume of applications the courses get. In some cases will be entry test scores and if he can improve those a lot that would definitely help.
Look up the offer rate for courses - he seems to be targeting 4 out of 5 both times that have low offer rates. That's risky. What DD did was just apply to Oxford and Bristol first then waited for Oxford result before adding more. Otherwise I would do more than 1 safe choice.
Gap years can be great but work experience at the moment its not the easiest climate and have a look where the opportunities are. I think best ones maybe London based which is very challenging if you aren't commutable to London due to accommodation costs. If they already have a job it maybe could continue that, that is what DD would have done as we aren't commutable. Around here there are opportunities still but not directly linked to finance, see what its like in your area unless there's a way can live in London. Abroad is worth considering and languages are useful but if you haven't got a good base in a language already not sure what chance there is you will pick one up.
If he gets 3 A stars I think he would get Bristol offer again, below 3 A stars its less certain. Some people do get in to Oxford second time round, maybe a few each year, but several I have heard of had offers first time applied, grades went down (I would assume special circumstances here), they retook or added got a second offer and got in. Though this is only from online forums so can't be 100% certain. Its a difficult one, I know DD in the same boat, would have wanted to try again, and I think a gap year could have been good, but its high risk as to whether it results into the most competitive options. People I know at Bristol are very happy though do a lot of partying every night. I would not be concerned for career options from Bristol though if he wants something very specialist you might stand slightly more chance from LSE or Imperial and being in London may help for London based jobs a bit. Many economics / finance jobs are London based and personally I would prefer to go elsewhere so you experience different places but its personal preference. Once you have the first job and experience places are a lot more concerned with your experience and rarely ask exact content of degree. Same with A levels nobody asks once you have a degree. Either option could work, its just thinking everything through.