It's doable, as you say, further down the CS league table.
Some, like Newcastle, 'encourage' A level computing (which your DS is doing anyway), and also require GCSE Maths (grade 6 in case of Newcastle), others have less stringent requirement (Kent, grade 4 Maths GCSE) etc.
One thing worth looking at is their syllabus. Kent with less stringent maths requirement still covers a decent amount of prerequisite maths in the first year (linear algebra, set theory, statistics, proofs, etc). Similarly for others too. So it's not possible to avoid maths entirely in a core computer science degree program, at least in first year.
That said, all of it is applied maths though, do not make up majority of the course content (even in first year), and I would imagine the universities will have good support for those modules, given A level maths isn't in their entry criteria.
Regarding career outside universities, I work in this sector and hire CS graduates, and haven't seen any preferential treatment for graduates with maths heavy CS degree. For sure a CV with Imperial or Warwick attract attention and will get an interview relatively easily, but for vast majority of CS graduate jobs in private sector, maths is not that relevant. There are some niche areas where its useful, but these roles often get filled with people from Maths or Physics background anyway.