score:5
You can, but you should expect to spend many hours on the bus/train. The fare is 13-15 AED (2.7-3.1 GBP) each way. The train seems to be slightly faster, but it may also involve more connections.
I'll give an example trip. This trip is estimated to take roughly 3 hours and 20 minutes each way.
From The Dubai Mall 01, take Bus 28 in the direction of Lamcy Plaza. Get off at Oud Metha Metro.
From there, catch Bus E16 in the direction of Hatta. Get off at Hatta.
From Hatta Bus Station 01, take Bus E16 in the direction of Sabkha. Get off at Etisalat Head Office.
From Etisalat Head Office 1, take Bus 27 in the direction of the Dubai Mall. Get off at the Dubai Mall.
Don't use those particular instructions, though. It was just an example. Use this travel planner to get up-to-date times and the perfect route for you.