I did an OU course several years ago and the end result would have
been a BA. Has this changed?

Yes. The preponderance of scientific, engineering or arts units determines
if the result is a BA, BSc or BEng. There are also named degrees that
require you to complete specific named courses. You can get a BA (Honours)
History if you take A220, A221, AA312, AA303 and a few other options, for
example.

Christian.