FYI the cut-off date for determining school year in the UK is 31st August of any given year. Children born 1st Sept 94 - 31st Aug 95 are currently in Y11, those born 1st Sept 93- 31st Aug 94 are currently in Y12. So from what you've said, you'd be looking at Y12 entry not Y11, which will improve your options a bit. But it will be tricky, no doubt about it. From about 14upwards is where the rubber really hits the road in UK education, adn it's focussed very specifically on passing particular sets of exams.
Y11 is the second of a two-year preparation for GCSEs, which is a pretty full-on set of public exams taken in the school year the child turns 16. A LOT hangs on it for the individual child, as well as for the schools, obviously. So the work will be very specifically geared to that, with lots of coursework and timed tests, all of which will be very closely tied to the syllabuses they've been studying.
I'd have thought most halfway decent schools following a mainstream UK curriculum (ie not an international school) will be very reluctant to take a new pupil into Y11. Most good schools won't have any spaces anyway, and the ones that do have spaces will be the schools no-one else wants. It won't be much fun for the child, and the school will struggle to make adjustments for a newcomer, especially if she hasn't covered the same curriculum. The kids will also finish being taught in about May, after which they will be on study leave.
HOWEVER -- if she is already 16 she would probably go into UK Y12, which is the first year of A-level courses. But at this stage most UK students will only be studying 4 subjects, which they will have chosen the previous summer. The sixth form application process is taking place round about now, so if you're looking at Y12 entry you should get cracking. But they will not be charmed by the revelation that you're only staying for 6 months, as sought-after schools will be over-subscribed with people wanting places for the full 2 years. Also bear in mind that you won't get anything like the breadth of curriculum you'd get at a US school unless you choose a school that offers IB. But even they might be a bit twitchy, because of the need to get their own pupils through exams. And again you'd have the issue that the good schools will have filled all their spaces.
I think you'd probably be better off going the International school route, if there is one nearby. Colchester is commutable to London, just about, where there are American and international schools. Otherwise look at further education colleges, which have a much less school-y curriculum and may be more flexible.