Strictly speaking, you can do A Level Maths privately since the exam boards don't require specific GCSE grades to study it (yeah, I'm annoyed as well).
You can alternatively try to persuade your college to let you study it since you're not off the required grade by that much.
The alternative to doing A Level Maths privately would then be to do a foundation year in engineering. The foundation year courses can be flexible with what engineering course you can later do, but they are a complete pain when it comes to transferring universities should you want to do your degree elsewhere.
Do note, some foundation year courses might only accept you if you picked the right subjects but missed the grades they asked for.
Other alternatives include:
•
Doing an engineering Access course - need 15 credits in maths and 15 in physics (if you didn't do physics at A Level)
•
Doing a BTEC in engineering - not as ideal because more universities accept A Levels
The other thing you would have to bear in mind is that maths and engineering are predominantly an exam based subjects pretty much all the way up to master's degree level. If you have exam anxiety, it's something you would need to really work on. If that doesn't resolve then it wouldn't make much difference even if you managed to get onto A Level Maths or onto a degree for engineering (and these tend to be more difficult).
What I'm surprised with is that your college would have lower requirements for physics, which is considered mathematical and en par in difficulty with maths.
In terms of studying in Canada or US, note that their SAT is similar in equivalency to our GCSE Maths and English Language to my understanding. Then the fact if you have studied A Levels, you are essentially have completed in their first year of Associates's or Bachelor's degree. I think you typically start picking your majors and minors in the 2nd or 3rd year.
You should also be able to get funding from the UK government to study abroad, but you would need to check on that.
Personally, I would speak to the college first to see what they say. If they say no, for whatever reason, then consider your other UK options before looking abroad.