You don't need further maths for engineering or maths. Obviously it's useful, but it's far from the end of the world - you'd eventually get taught it and beyond at uni anyway.
I mean, I don't think there's a lot you can do. You could do AS further maths next year, provided that your AS maths grade is good this year. If it's a school policy that's been fairly used on all students, there isn't much of a case, unfortunately. I'm sure you knew beforehand you had to get an A* to do Further Maths anyway.
Lastly, Maths A Level in itself is quite difficult. Loads of people in my class with A*/A ended up with C/Ds, so you might also have to consider whether you'd be able to cope too.