I doubt gcses were the problem with your application. I had 667777889 and got an offer, though I didnt apply to law so it could be different.
Oxford looks at grades in comparison to the school you attended, so if you went to a really high-achieving school then perhaps it could be an issue. My school had an 'attainment 8' score of 41, which is below the national average. Only 59% of my year passed Maths and English (and only 33% achieved a 5 or higher).
Also, with Universities with as many applicants as Oxford, it may just come down to numbers. They have to shrink the pool enough for interviews to be feasible, so dont beat yourself up over it.
You could take a gap year, however you would need to occupy your time or it would be a waste. Perhaps finding work experience or something cool related to your subject would be a good idea.
Why do you want Oxford so badly? Is there not any other university that could give you whatever it is you want from Oxford? If its the area, there are other universities nearby. If its the prestige, there are many other respected russel group unis. If its history, there are other universities that have been around for quite a while, though Durham is the only old one I can think of off the top of my head. If its the collegiate system, York and Durham have that too.
If you do reapply, be aware that you could be rejected again so make sure you have backup unis that you actually like. Did you apply to anywhere other than Kings that you might like?