My brother had a break between year 12 and 13 (2013-14 year). He started the year and got to around January when he had a mental breakdown and his school (admittedly private) agreed to let him take the year out and restart year 13 the next academic year.
However, this was before the law changed regarding staying in education until 18. There are though ways around this if you really think you need it. My brother could hardly get out of bed. Other people I know had to have stints in eating disorder units or had periods of psychosis (hearing voices, etc). It isn't something to be taken lightly, but if you get a doctor's note and you're able to work out a "home schooling" agreement then you could probably do it.
Whether it is worth doing so before your GCSEs is something I'd question though. There are things you learn now that you'll need then. In maths, for example, things you learn in year 9 and 10 will be needed in the exam. Same with parts of the three sciences (at least how I was taught them) and therefore taking a year out may cause difficulties here. If you've finished year 10 this will be even more difficult and probably cause you even more stress when you try to go back.
If you really need a year out I'd suggest waiting until you've finished your GCSEs, and then only if you're not doing a subject that requires knowledge of the GCSE as a foundation (maths, sciences). Also as someone who's just finished her A Levels, I will say that it's possible to do your GCSE exams without stressing too much about them. Most people I know got through them with barely any revision and came out with pretty good results. I still haven't read Northanger abbey and managed to get an A*. If you build it up in your head as this insurmountable task then you'll be stressed. Try to avoid thinking like that and you'll thank yourself later