There should be someone at your current/last institution who can point you in the right direction. There is also plenty of information on the internet. A site ending .ac.uk will be an academic site run by a university, college or other "official" academic body. A site ending .gov.uk will be a government site. I would be surprised if there were many places left for this year, particularly if you are set on one particular course of study, so you may need to spend a lot of time phoning round looking for vacancies then your choice may be between applying for what is available or waiting a year.
Here is one starting point. It may not give the exact information that you want but you can get contact details from here.
http://www.ucas.com/students/nextsteps/
UCAS is more geared up for first degrees but the site is still worth a browse.
The deadline for applying to many courses is mid-March, some ask for earlier applications. At this stage, there will still be a few vacancies where someone has changed their mind, where a course was less popular than anticipated and where the institution is looking for exceptional candidates.
If you decide to wait a year, you should start the application process now.
If cost is a major factor, you should look at some courses outside the South East.
Some post graduate study is done in conjunction with employment at a university but, again, most of the appointments for this year will have been filled. Depending on your first degree, the jobs section here may be worth a browse. Certainly you'll find something worth reading in the publication.
http://www.timeshighereducation.co.uk
I wish you well but you need to keep your head up and look for something worthwhile in the event that you can't find exactly what you want.