I was in a similar situation, got rejected first time around, took a gap year (for unrelated reasons) and decided I might as well give it another shot. And got in second time round. It's definitely possible and having your grades already is always a positive. However I'm not sure if it's the best idea to take a gap year for the sake of reapplying. If you didn't make, it you might end up feeling as though you've wasted a year of your life. I'd only say it's a good idea if you have some ideas of stuff to do, whether that be working, improving yourself, or travelling, so that you come out the other side of your gap year feeling happy with your decision, whether you get in next time or not! And it's definitely a good idea to have some geography related things planned that you could talk about in an interview or personal statement.
Side note, my insurance choice uni, UCL, which I was going to attend if I didn't take a gap year and which offered me a place the first time I applied, actually ended up rejecting me when I reapplied. So if I hadn't got into Cambridge, by God's grace, I wouldn't have had that to fall back on. I think that you probably would get into manc again if you reapplied, especially with 3A*a, but it's always a small possibility that you may not get your insurance second time round!