Visa on arrival for Brits is for 30 plus 9 ie 40 days. As in you must leave on day 39. To renew, the best option is to go to Hatta and across to Oman. Pay 50 aed to get an Omani Visa. Then return. You are ok for another 39 days. Don't go down the fine route. It is 200 aed for the first day. 100 for every subsequent day. No limit.
It takes 4 hours or so to go to Hatta and return to Dubai
Good luck