This is kind of complicated. There are in theory two stages of acceptance at a British university: getting accepted, and then getting funded. Generally, any student can get accepted if and only if a supervisor says they are willing to take them as a student. Getting funding is harder because that is in more limited supply. If funding is allocated to the department or faculty, then probably it will go to the best student, but it may well go to a particular supervisor instead, e.g. a new young lecturer that is seen as needing extra support, or someone whose current research project is seen as important or promising, or just someone who hasn't had a student for a while. But quite a lot of funding is won by particular supervisors themselves, in which case they advertise a studentship like a job, and review as many applicants as they can and pick the best one. This can happen any time of the year. Actually, so can the departmental funding -- you never know when the university, government or some benefactor will suddenly come up with money they want spent.
I said "in theory there are two stages": in practice, sometimes a prospective student (perhaps one responding to an advertisement, or just one who's folder has been sitting on a desk a while) is clearly the best applicant for some funding, and there is a sudden rush to formally accept that applicant so that they can be put forward for the funding! In the specific case you mention, there will normally be a competition between supervisors for the funding (not all of the advertised possible positions might be filled) so there will be a deadline that allows departments to compare the applicants. But a truly outstanding applicant might still be made an early offer, if the committee is certain from past experience that they are likely to get the offer anyway, and if they are concerned the student might get snapped up by another university if they wait.
In general, and in any country, it's important to apply to multiple universities because there is such a large chance component in getting accepted, even if you are very good. Certainly in the UK you should contact specific supervisors in advance and show them convincing evidence that you will help with their research and are likely to get funded. This means showing you've read (or at least read about) their work, and that your record to date is very promising (e.g. already having published papers helps a lot with university funding.) If you don't already have an outstanding resume, it might be a good idea to pay for a masters degree and then try to get a publication out of your dissertation project, or try to get a lab position where you can help with publications.
If you've done all that, and are not sure you can wait to find out if you got the funding you most want, be sure to let the person who might be your supervisor and your director of studies know that. Not every supervisor will know all the options, but the director of studies should, but your supervisor is your main champion. Good luck!