You'd need to contact the individual universities if they'd allow you to start a course in January as opposed to September. Same thing with applying now for a course that starts in a month or so.
That said, moving and staying in the UK via student visa is difficult. The PSW route is pretty much closed, and it wasn't permanent anway. Also many of the work visa routes are also closing. Of course, if you have $$$$ to invest you may be in luck!
You could come in for a year, but it is getting more and more difficult to find a route to stay.