I know you're stressed out but it's called a "requirement" for a reason. A 7 in Physics HL is very impressive and useful for an engineering application but really it won't compensate for not having the base knowledge for an engineering degree you get from HL Maths, that the universities you mentioned expect you to have. You can apply to those universities, but your chances really aren't good. Even for an unpopular course like engineering, these unis aren't exactly desperate.
Tell you what, why don't you put down 1/2 unis that require IB HL Maths as your "high-risk" choices, then the other 3 should only require IB Maths SL. If you don't get into your 1st/2nd choice unis on the basis of no Maths HL, but still want to go, you can take a gap year, and during this gap year do full A-level Maths or you could consider distance-learning Advanced Higher Maths (a Scottish qualification that is considered equivalent to A2 Maths and covers a fair bit of Further Maths topics too), and you can apply during your gap year.
As for Civ/MechEng course that don't require HL Maths, well, there are courses. Look on a Civil/Mechanical Engineering league table and look at some of the unis towards the bottom, they tend to be quite unpopular so have lower entry requirements. Examples are like Greenwich, Nottingham Trent, Sheffield Hallam etc. They only require something like 200 UCAS points and no A-level Maths, so you'd instantly get in there.