You are in your mid 20s so you are still quite young, and still have a reasonable chance of getting onto entry level jobs.

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"?

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"?