For going to another uni rather than changing course within your current uni, it's possible but not without caveats.
If you wanted to go from e.g. year 1 in uni A to year 2 in uni B, it's absolutely NOT guaranteed. You would need to contact uni B to see if they would accept you to transfer into year 2 of the course.
For restarting in year 1 at uni B it's usually easier.
In either case you would need to reapply through UCAS - and direct transferring you would need to contact the second uni BEFORE submitting an application.
I would recommend reading the transfer FAQ sticky thread in the applications forum.