I'll call BS on degrees being played down for entrepreneurs - and certainly the idea that they mostly don't have them... unless you're counting your local shop keepers, hairdressers etc...
Most tech start ups are founded by people with qualifications and industry experience not university drop outs or geniuses without degrees etc... don't mistake the Bill Gates, Zucks etc.. for the norm - anyway they were originally very capable students at a top Ivy League uni who dropped out
because their businesses had already become successful.
Obvs if he's got some super cool, disruptive, moonshot idea that achieves some rapid growth initially regardless of funding then VCs/Angels etc.. will perhaps be inclined to throw money at him regardless - but the Zuck/FB types are the exception not the rule.
If he's hoping to set up a small software house, taking on paid projects etc.. or being an independent contractor etc.. then having some credentials/experience would still be useful.
If instead he's going for some high growth start up that requires funding then this might mean leveraging the [non-brand name] undergrad degree to get a [brand name] MSc and in that case better to sack off the soft subject (Business studies) and combine CS with maths - something that will be much more helpful if you're going to get into something serious/deeply technical... I mean that could be like a 5-6 year plan - Computer Science&Maths join honours or similar over 4 years part time then 1 year MSc course somewhere decent (or 2 years part time), then leverage your MSc/dissertation into a start up - people certainly do that at the moment, there are some obvious areas that are hot right now and some serious funding is available (just take a look at the various incubators/seeding programs and the start ups there - you'll find people who've met via university etc..). Not to mention there are academics in Oxbridge/top London unis who are involved in start ups and people at those universities who can help with putting you in contact with the right sort of people.
Also note there are more and more opportunities for flexible study popping up and govt funding (loans to cover fees) available - Oxford offers some flexible/part time MSc program (Software Engineering, Security) and Imperial just launched an online one (ML/Data Science), UC Dublin has one (data science related), various respectable US universities offer them Georgia Tech has a well established one, endorsed by President Obama even!
etc...
I mean it's kind of a long game and would require a lot of work (don't underestimate this) and would be better if OP started acquiring some relevant work experience now too so he has 3-4 years of experience working in tech while completing the undergrad study) but for a higher chance of success then getting the mentorship and funding etc... via an incubator type program would seem to be a better option than say taking pot shots with say random apps in iPhone/android app stores or trying to get a web based business out there, by yourself, organically.
While technically you don't need a degree (or degrees) it can be incredibly useful to have them (better though if it is from a good brand, comes with some experience etc..) - the routes available to you in terms of getting connections/funding and your credibility can vary quite considerably compared to just going it alone and hoping for organic growth.
If aiming at being self employed/running a small tech business rather than start up then the above doesn't apply so much but at least having a BSc and some work experience in a tech firm or similar would be helpful/give credibility before taking on projects/clients independently.