I think the answer is yes.
Further Pure and Mechanics modules in FM are really heavily involved in Engineering studies as it provides a solid foundation for the physics/maths knowledge that you need in university, not to mention that your uni application will look stronger with FM in it.
My advice would be continue doing A2 level Maths, Physics and Economics and pick up AS level Further Maths (Focus on FP and Mech modules, tell the teacher not to include Stats/Decision if possible) as a fourth subject in Year 13 if you can handle the workload.