What you're proposing is similar to what I did.
I started Yr 12 doing French, Spanish, Law, and History.
Halfway through the year I dropped Law and French.
I started Classical Civilisation in Year 13.
Then I stayed for an extra Year 13 to finish off Classical Civilisation. As that wasn't enough to fill my timetable sufficiently, I also resat French (I'd gotten a C but wanted a B), and did GCSE Italian.
I then took a gap year, and started uni (University of Leeds) 2 years "late".
So yes it's doable, or at least it was in my case. Although unis do prefer you to take all three A-Levels together, if it's not an oversubscribed course you're going for, you have a high chance of being considered regardless. Unfortunately I do think that psychology is very popular at unis, so they may be more picky, so do bear that in mind.