"Data scientist" is a really vague term. It's really a matter of looking at your current skill set and interests, and seeing where they fit.
For example, many CS grads don't have strong stats/maths backgrounds. However there are still many "data science" jobs open to them. For example, you can work on the tooling that goes into storing and processing data (e.g. Hadoop), or you can build visualisations. If you want to work on, say, data analysis you need to have a stronger background in stats.
Some CS departments require undergrads to do the typical engineering maths sequence (Calculus, Linear Algebra, etc.) but many don't. Lots of PhD students in machine learning have undergrad degrees in physics, maths, or engineering.
Where I did my PhD (the top ranked CS department in the UK by a recent survey) the undergrad students did one maths courses in their entire degree, with most of it being discrete maths (IIRC). This really limited the ability of students to undertake research in machine learning or theoretical CS.
Since your based in Birmingham I can take a good guess at where that is, because I studied there and live in birmingham. And I agree, but the machine learning/A.I modules themselves had to have maths placed within them.
Nice to see brummies on hacker news. Since your start up guy, I guess you hang around faraday wharf?
For example, many CS grads don't have strong stats/maths backgrounds. However there are still many "data science" jobs open to them. For example, you can work on the tooling that goes into storing and processing data (e.g. Hadoop), or you can build visualisations. If you want to work on, say, data analysis you need to have a stronger background in stats.