PhD study for staff? I've recently been offered a research contract in a UK University within a Mathematics and Statistics department. I've been trying to get into Mathematical research for a long time, but in the mean time to continue research, publish, and so on, and to pay the bills I've had to take research based academic jobs in a varied number of departments in a number of Universities from Engineering to Sociology ! My background is Computer Science, in which I have a PhD.

My question is: Is it likely that a UK University would permit staff to study a part-time PhD in a new field within the department, e.g. Mathematics. If so, would fees be wavered? Or would this not be allowed since I already have a PhD in Computer Science. I've had a rocky road to Maths, for one reason or another, and had to take jobs I sometimes felt divergent to where I really wanted to go, so it would be nice to "tidy up" the loose ends.
If there is a gap in your knowledge, and there is a course being offered that is a good fit for you, you could either enroll in the course or audit the course.  One course per semester maximum, please, so that it is clear where your priorities are.

One PhD is enough.  Math and computer science are close enough.

Yes, your self-confidence will grow as you build up a publication record.

Congrats on getting the job!