Medicine in uni to research later on

Great question, bit of a confusing course structure.
After 3 years, you earn a BA (Bachelor of Arts - this is what all Cambridge undergraduate bachelors degrees are, including natural sciences, maths, ect) in whatever subject you choose to study for 3rd year (its similar to intercalating at any other med school, except you have to do this). Generally people study biomedical sciences of some kind.
After 6 years, you earn a MBBChir (Bachelor of Medicine, Bachelor of Surgery). This is what all medical graduates at any med school get. You need this degree to go onto the NHS Foundation training programme (FY1/FY2), and therefore need it to become a doctor of any kind in the UK.
After the 3 year degree, you could feasibly finish the course there and go into 'research'. You wouldn't be qualified as a doctor, but could go on to study a Master's in a biomedical subject, and then a PhD, leading onto a career in research in academia (attached to a university) or research in industry (working for a company, like AstraZeneca). Exactly what you research will depend on what you do in 3rd year/ masters/ phd, but could be a range of things related to medical research (like drug development or public health research).
However, for most types of clinical research (where you're working as a doctor as well as being a medical researcher, or carrying out research involving patients), you will need to go onto complete the 6 year course and qualify as a doctor.
You could work in medical research without the BA, having studied medicine anywhere else, or having done a Bachelor's/Master's as an intercalation at other med schools (I've seen someone point out that other med schools allow you to intercalate for a masters, which would be more beneficial than the cambridge Bachelor's).
I think a key benefit of the Cambridge course is that you can leave after 3rd year with a Bachelor's and go get a normal graduate job with a biomedicine degree. Most med schools don't allow you to intercalate until 3rd year.

To generalise the above informative post, for any medical degree it takes 5 or 6 years (as a school leaver) you can go into research after completing it regardless of whether you do a 5 or 6 year course. Intercalation may be useful if aiming for research though. Also some unis allow you to intercalate a PhD e.g. the UCL MBPhD.
Technically you can go into research immediately but you need to complete your F1 year within a certain length of time after graduating to become fully registered with the GMC or you can never get full registration as a doctor, and if you're doing F1 it's probably easiest just to finish the whole foundation programme before starting your research degree (assuming you hadn't done it during the medical degree).
Note there are also formal academic training pathways in medicine which facilitate a career as a clinical academic and I believe most will get a PhD or MD(res) while in those tracks. These are the Academic Clinical Fellowships (ACF) and Clinical Lectureship (CL) tracks.