A lot depends on how good he is at maths. Some degrees are very maths heavy and they lead to jobs which are maths heavy. But the expectation, normally, to get onto one of these degrees is A* in maths if not FM. Not everyone will want to be, or is able to be, a quant.
There are lots of career openings for people with other skills who have graduated from a good University and who have a sound understanding of economics. He only needs one place, and if he has found five he is interested in applying to, that is fine. (And don't limit it to RG. Bath, say, is very good. I don't know if they need maths.) I might also broaden the search to economics and finance or economics and management or economics and politics if that is where his career interests lie.
That said, economics can be fiercely competitive, and many courses oversubscribed. Good Universities are able to demand good grades.
I might try a two tier approach. Apply now, where he can. (Only places he would really like to go to, and three or four within his predicted grades.) Work like blazes to get the best grades possible. In the meantime plan for a Plan B by researching different ways of sitting maths. Some private providers allow for tuition in 2 batches, one intense one at the start of the academic year which enables them to write an informed grade prediction, and then another intense couple of months before the A level itself, with travel in the middle. Or there will be on line options. If he does not get a place either via UCAS or clearing, launch Plan B.
You might also look at courses which have both a BA and a BSc, or perhaps joint degrees, and ask if there is any scope to switch if you choose the right courses in the first year. Big departments might have a bigger range of courses and more flexibility. But honestly I have never heard anyone say anything other than "I have an economics degree" without specifying that it is a BSc. If you have that degree you will be assumed to have the equivalent of maths A level. If an employer really wants someone technical who is adept at financial maths/statistics, they will be looking for first degrees from specific Universities (probably Cambridge, LSE, UCL and Warwick) or a good Masters.
He might also be warned that many find the maths part of economics particularly dry. Though not everyone. DS, who had never thought of himself as good at maths, found himself loving it at University, and eventually graduated in econometrics