Is there any appropriate way to offer cash to a lecturer or TA for private tutoring? Due to financial issues, I've had to work in order to support myself alongside my degree, and unfortunately due to work obligations I've had to miss some lectures and classes.  Due to not spending much time at the university, I also don't have many friends who would be willing to help me catch up.

Would it be appropriate in any way to ask the lecturer or the class TA to help me on a 1-on-1 basis?  I think I've managed to fall behind sufficiently far that I would need several hours of help to catch up -- could I possibly suggest to the professor that I can offer you £50/hour for your time?  I don't want it to be construed as bribery or anything inappropriate -- I just want to pay the person fairly for his/her time.

Is there an appropriate way to do this?  I know that in my high school some students paid teachers for 1-on-1 tutoring, but I'm not sure how it works in university?

For context, I'm in the United Kingdom, I'm doing a master's degree, and the end-of-term examinations are administered anonymously (i.e. the person grading does not know whose paper he/she is grading).
At my university in the USA, it would likely be illegal for the instructor or the TAs of the particular class to participate in this. There is just too much of a (perceived) conflict of interest since they are evaluating you for a grade for the class.

However, there would not be anything barring you from approaching a graduate student who was a former TA for the class; nor would there be a problem in approaching an instructor at another institution or someone who is at your institution who is not teaching your section of your class that term. You could even ask an upperclass student who took the class last year to tutor you.

Your department secretary may be able to connect you with a grad student who needs a few extra dollars and isn't in the conflict-of-interest position to tutor you directly. Or post something in your local craiglist or student bulletin board system.