I have a BSc in Pharmacology and am now doing an MSc in Molecular Neuroscience.
I would like to do a PhD in a related field, although I have read horror stories of people not being able to find a job after completing their PhDs, which really put me off.

What I really want from a PhD is better employment prospects and salaries. If I got accepted into a prestigious university (Oxbridge, UCL etc) would that be more attractive to an employer, or do all employers just see PhD and think "overqualified"?

It's best not to do a PhD to get a better job or salary these days, but of course this depends on your field and what type of job you are looking for.

But let's say I apply for a big pharma / biotech company.
Wouldn't not having a PhD mean I will reach a "glass ceiling"?

No, as there will always be the likes of CIA, MI5, Mossad, Haliburton etc.

I agree with TreeofLife, pursuing a PhD for the sake of a better job doesn't seem a good idea. For doing a PhD, one should have a strong reason to devote a long period of one's life. A PhD would take more in the world of academia, and I understood, you want to increase your capacities for better and high ranking jobs. You can develop your skills and competence in your field by going for training courses, workshops and even doing another Master's degree..

No more or less than anyone else- BUT they often involve long-term projects of immense detail, which they recognise as being similar to your doctorate (which also proves you capable of the work). Don't concentrate on them though,for employment, yet; often, they will come to you.