I am glad you are taking @Patriciastaser ’s advice because it is definitely the way to start.
But I wonder what else is going on here, and I think DS should do some self assessment, bearing in mind that there are no right or wrong answers.
We are a highly ranked STEM School and we have many students who missed out on Oxbridge and Imperial. Sometimes an MSc from one of those institutions represents a validation that they didn’t get the first time. It can be important to a student’s self image and confidence and this can play out in all sorts of ways. It might be good for DS to think about what this MSc represents to him.
Ultimately, an MSc in CS is either a stepping stone to a PhD or an employment credential. I will return to the first case below. It sounds like DS has bagged a great job! So this is an odd time to be pursuing an employment credential.
It isn’t clear to me how much CS he is actually doing vs how much he would like to be doing. If that’s an issue, an MSc down the line may make sense. I would think getting what he can out of this job first is a good idea for career purposes.
We may be heading for another financial crisis. Has DS considered that even though the MSc he is focused on is a great credential, there may be no jobs at the end if it?
Now, if he wants an MSc he wants an MSc. I don’t think these institutions should be the only choices, although they may be the most desirable (eg Birmingham is very highly ranked and well thought of by employers).
I think the Maths may be a bit of a problem but the admissions tutors can guide on the question of formal remediation. In their place I would be more impressed if DS did some upper level Maths related to CS, and there is plenty of it. Again the admissions tutors can advise, but one useful field to focus on broadly is discrete mathematics , another is mathematical logic. These are used at more advanced levels of CS. Also abstract algebra and number theory are used in cryptology and cybersecurity. OU has course units in all of these.
DS can’t do it all! He could do one or two course modules to show enthusiasm.
Will he have time for any of this?
If he wants a PhD he may need to do it at some point, because he will probably need an MSc first. Otherwise, I think he needs to weigh up the pros and cons of leaving a good job in the current fiscal climate carefully. He need not rush into the MSc as long as he is staying connected to tech.
Best wishes to him.