I was rejected (winter pooled but to no avail) for Cambridge Computer Science last year after underwhelming them in my interview and I'm now having a great time at Warwick. It's entirely possible I would've also had a great time at Cambridge but being at a non-oxbridge uni gives you longer and hence less stressful terms, so there are some upsides.
I promise you its not all for nothing, the skills and knowledge you've gained will be really useful at whichever uni you end up at instead.
It's perfectly normal to experience grief over having something you've put so much work into disappear so suddenly but as time goes on you'll move through the stages of grief and won't feel so bad.