My main contribution is probably only obliquely useful. I collect job packs for computer science and related roles (adverts, person specifications and job descriptions) and 'trap' them so that people can browse them at their leisure.
The useful aspect of it is that I've got about 70-80 of them in different sectors so while the jobs themselves are closed the companies may be worth investigating to see what else they're offering https://techdevjobs.wordpress.com/jobs-organised-by-sector-theme/
Has he looked at roles within his own university, for example helping as a teaching assistant for the first year undergraduate modules?
The Find A Job website from DWP (https://findajob.dwp.gov.uk/search) can be filtered by location and keyword too.
Prospects also has a page called What can I do with a computer science degree, which might open up his search options a bit https://www.prospects.ac.uk/careers-advice/what-can-i-do-with-my-degree/computer-science
Also can he use Google Maps to draw a local imaginary circle and zoom in to see some companies he might not be aware of https://www.google.co.uk/maps. I'd assume that almost all of them will use computers in some way and possibly he could be useful to them, though it might be more at the web design or databases end of things rather than his main interest.
I'd also certainly echo others' suggestions to get any job.
Speaking of Google is he using Google Alerts https://www.google.co.uk/alerts to bring new job adverts directly to him? He'll need a Gmail account for this and can put in some keywords and then refine the search (e.g. computing jobs would result in being swamped). If he's got Gmail then I'd also recommend creating a Google Doc (I mean, any document would do) then bunging in all the job vacancies pages he comes across, then he can cycle through them every few days. He might be able to deploy pages' RSS feeds if they have them.
The Global Disability Innovation Hub doesn't have any paid roles at the moment but are always on the lookout for people with lived experience to join their panels, to give input on improving design of assistive tech / ICT for disabled people. Might be an interesting thing plus networking opportunity if he learns that he has ADHD https://www.disabilityinnovation.com/who-we-are/work-with-us
Raspberry Pi are doing some interesting work in supporting schoolteachers who are teaching AI and machine learning, I don't know if they're taking people on but might be worth haunting their website and familiarising himself with their Experience AI suite of classroom activities https://experience-ai.org/en/
If he's interested in games design there's the Entry Level website https://entrylevel.games/. At QMUL (London), where I work, we have a Games AI department that specificallly focuses on research https://www.qmul.ac.uk/eecs/research/research-centres-and-groups/game-ai-research-group/, don't know if there are graduate jobs though unless he's planning on applying for a PhD - our jobs page is https://www.qmul.ac.uk/jobs/vacancies/
This is something I wrote for GCSE / A level students regarding work experience but there might be something useful in there https://teachinglondoncomputing.org/school-work-experience-some-ideas/
Networking with various hackathons? Helping out at code-clubs for experience and CV fodder? Teaching at adult education colleges? Sessions in local libraries? Tutoring? (Also tutoring maths, I'm assuming he knows his way around that quite well).
Good luck to him :)
Jo