Psychology Degree - BA or BSc...?

I'd do the BSc (well, I literally did do a BSc in psychology). It also needs to be BPS accredited so you can gain Graduate Basis for Chartered Membership, that will enable you to go on to do counselling psychology or forensic psychology. Most courses that are BPS accredited tend to be BScs from what I remember.

Having just returned from an interdisciplinary conference, I'd suggest the BAs—many of which are BPS accredited (e.g., Lancaster).

Why though?

It's better to get accreditation right off the bat in your undergraduate degree, or you won't be able to go in to do a postgraduate course that will give you the right to practice and use the title "counselling psychologist" or "forensic psychologist" - hence why you need BPS accreditation. You'd have to do a conversion MSc then the appropriate postgraduate course - it's just longer. BSc is better because then you'll understand the statistical/scientific side of psychology more than BA students would.

I'm filling in my ucas choices and I want to do a degree in Psychology but I don't know if I should apply for BA Psych or BSc Psych. Which one is better or gives you a higher chance in getting into counselling/forensic psych?

Have a look at the course specification for Lancaster's psychology BA course:

That particular course includes a 'Forensic and Investigative' module as an optional specialism; it is BPS accredited, which would position you well for counselling; and it also offers neurocognitive and psychopharmacological options, which would serve you well should you later pursue clinical psychology or psychiatric medicine. You'll also notice that they don't eschew research and statistics training.

My suggestion is also driven by recent developments in the field that will lend to increased demand for interdisciplinary perspectives and approaches.

It depends on what you want to achieve with your degree. As @Avaia said, you would need to do the BSc to become a psychologist.
A BA in Psychology is quite subjective and philosophical and I haven't come across one person yet who is doing a BA in Psychology in my uni. It is quite limiting and I think that it's not much different to studying philosophy.
The BSc covers things scientifically, of course; studying the brain, doing and looking at scientific studies, recording data, dealing with statistics and so on.