I've looked into this. For some unis, they require 3 Mechanics Modules in Maths, without either Physics or Further Maths. I've emailed a couple and offered 4 Mechanics units and still many require Physics. Many reply with Study Computer Science or Chemical Engineering instead (as I take Chemistry, Maths, Further Maths and Computer Science). CompSci could be a good option if you choose a BEng or MEng course, as it requires only Maths.
All take Maths and Physics. Few take Maths and Further Maths and even fewer, with just Maths.
An alternative route would be a foundation year or resitting a year and taking A level Physics.