@CaliforniaDrumming. I have posted the same, probably every year. The level of competition came as a big surprise to us, and clearly to others.
If he wants to go on to economic research (lots of jobs within banks and consultancies as well as the public sector or academia) and he has a maths bent, he should consider a reapplication rather than accept an alternative course first time round.
It will be easier with achieved grades, and much of the bulge problem should be over. However do not take silence from UCL and Warwick as rejection. It is actually a positive. Both will probably be using a gathered field approach. They reject and accept some immediately, but will hold onto the rest until all the applications are in in January. (And some start withdrawing after receiving a Cambridge offer.) They then start accepting some and rejecting some as they try to match offers to available places. Many will not hear until March. (DS got two of his rejections then as well.)
If he is interested in mathematical economics he might look at various maths with econ courses, and the levels of competition. (LSE give offer rates.) Certainly DS, who chose some sort of maths as his outside option, essential did the same first year as some of those in the maths department. He then opted to graduate in EME alongside some who had started in the maths department.
Almost all of DS's maths orientated peers ended up taking a Masters, so you could also look at the sorts of first degrees, MSc courses are looking for. (Normally the more maths the better, so the fifth option might be chosen to reflect this. Econometrics at Bristol perhaps, though Nottingham is also a good University.)
DS believes that his personal statement was not strong enough. Your DS could do things like look out for public lectures from places like the LSE that he could watch on-line, or follow academics in the areas that interest him most on Twitter as they will be tweeting and retweeting relevant stuff, as well as further reading around.
Then read everything you can find on University websites about the sort of applicant they are looking for, imagining that the first read is by junior admissions staff who have a score sheet with which to mark them by. So follow the University guidance making sure you have covered each desirable/required attribute and evidenced it.
DS is now in the US studying for a fully funded PhD in a well regarded University. He was also offered a couple of Research Assistant jobs, including one at Princeton. His peers seem to have done equally well and he now has a really good, and international, network.
The waiting and uncertainty was awful. But there are lots of ways to get to the same place if you have the aptitude and are willing to put in the effort. And in retrospect I am glad that this early experience of "rejection" happened when he was at home and we were able to support him. He has had plenty of rejections since, and will have more in the future. Ambition is a good thing, but it does bring the risk of rejection and there is a need to balance aspiration with a realistic Plan B, be it reapplication or accepting his fifth choice.
Good luck!