I think it is something that you must do and it is really fun. I went with the girls I worked with at Sweaty Betty and we had a blast!
My best tip for you to get a cheap punt is to haggle. The punting is very competitive and so you have the upper hand. If you can go during the week because Saturdays are very busy in town. Also I would plan to go on a summer day.
All the Best!
American to Britain