This depends whether you’re applying for ‘academic’ postgraduate courses (Masters degrees etc. in academic disciplines) or ‘professional’ postgraduate courses (teacher training, legal professional courses and others where entry is by postgraduate study, including social work).
Some universities have early application deadlines, others accept applications into the summer before the course starts, so always check with course providers. You can apply from early in the previous academic year, and it’s worth doing this for popular courses which may fill up quite early. Earlier application (before April) may be needed if you want to apply for funding, but again check with the course provider and see postgraduate studentships for information.
You apply to each university individually using their online application portals. This means you decide how many courses and institutions to apply for, unlike the UCAS first degree application system.
Application to teacher training is through UCAS Teacher Training: Apply and Track and for law professional courses by Lawcabs. You need to apply by a deadline, generally mid-January, to guarantee your application is considered by all course providers.
Application to other ‘professional’ masters degrees provided by universities, such as Archives Management, Museum Studies, Journalism, and Library/Information Studies, is as for other courses at the same university. Details are always provided on the course web pages.
You will often need to submit a personal statement when applying for further study. See below for more information.