BA to BSC psychology

Not necessarily. Does the uni offer both BA and BSc versions of the same course as listed on their website?

It's a moot point anyway because whether the degree title is BA or BSc has no bearing on what the actual content of the course is. Some unis (e.g. Oxford and Cambridge) only offer BAs, their degrees are just as if not more scientific than any other uni for those subjects with scientific elements.

For psychology the important factor is whether it's BPS accredited. You should focus on that more than whether it's a BA or BSc.

It offers both BA and BSc, and both are BPS accredited. But BSc is more scientific and statistical whereas BA is more historical. I prefer the maths.
There's obviously a difference if they offer both.

In that case you should contact the uni to find out if you can move between them and/or why you can't apply to the BSc course on UCAS.

Note that just because they offer both doesn't necessarily mean they are different either - for example LSE offers both a BA and BSc Social Anthropology, but the course and the course options are identical for each. It's just student choice which they graduate with.