You're studying the BTEC National Extended Diploma with predicted grades of D*D*D* ('triple distinction star') and you have a high grade in a construction qualification? I'm guessing the construction qual is either one of the old vocational A-Levels or a BTEC certificate in construction. I don't think that there is an A-Level in Construction, but please correct me if I'm wrong. I've taught a lot of A-Level Physics and BTEC Engineering / Applied Science, so I think I have a fair idea about the content of these courses. If you were one of my students I'd give you the following advice...
The mathematical demand of an engineering degree at Cambridge is like nothing that you have experienced in any of the qualifications that you've studied so far. Both in terms of the content and the style of delivery, it really isn't like anything you've seen in school. I'd strongly suggest that the only way of knowing whether or not you'd enjoy such a challenge is by studying A-Level Physics, Mathematics, Further Mathematics and maybe a few of the 'STEP' (Sixth Term Extension Paper) exams. It's not really possible for you or anyone else to know how you'd get on at Cambridge until you've tried to do the sort of thing that people who apply to Cambridge typically do. You need to think of the A-Levels as allowing you the opportunity to find out what hard quantitative problem solving feels like before you decide that you want to spend time and money at university pursuing an undergraduate degree.
To be clear, I'm not making any judgements about your ability to do well on these courses. You seem hard working and committed and I've got no reason to believe that you wouldn't be successful. In fact, you may very well be a fiendishly sharp mathematician and problem solver. You may already have been working on A-Level Maths problems for fun. However (and I can't emphasis this enough) you need to know what you're getting into and your current qualifications aren't designed to do that. When you say you could take a gamble on getting into Cambridge you're ignoring the possibility that after studying Maths A-Level you'll have decided that an Oxbridge application isn't for you. I'm not saying that this is going to happen, but it could and we have no way of knowing how likely this is.
On the other hand, you could go to a different university next year (likely starting on the foundation year to cover some A-Level Maths type stuff) and pick up a degree in four years. You could then get your career started and begin earning money. It's true that an Oxford or Cambridge degree does confer some advantages. Then again, I work with a guy who studied engineering at Cambridge. We take home the same pay. I studied physics (and drank heroic quantities of beer) in a town you've never heard of. Another of my co-workers did medicine at Bristol. Same story.
Right now you might be thinking 'Yeah, but I could go to Cambridge!' Sure, but we don't know if this is something that is realistic or even if you'd want to after you've gained a better idea of what's involved.
I'm trying to give you the best advice I can so that you can make the best decision - not to discourage you! If you want to put yourself in the position of making a competitive application to a famous university then go for it. You've got time on your side and nothing to lose. The worst possible outcome would be that you'd have picked up a few A-Levels in Maths and Physics. However, it's worth pointing out that no matter what happens it seems likely that you'll end up at a university somewhere and its the study that you do at university level that will set you up for your professional engineering career.
Your current qualifications are at what is known as Level 3; that's the same level as the A-Level Maths and Physics qualifications that you're thinking of taking. What this means is that you'd have spent a long time studying at the level that is set up for people to pass through on their way to something else. You might consider this to be standing still for too long, or you might think it's been time well spent sharpening your focus and getting you ready for whatever comes next. I don't know which view is the most accurate for your situation.
Success over a lifetime depends on much more than which university you attend. It's true that most of the people I know who went to Oxford and Cambridge are (by my own modest standards) wildly successful - but I can say the same thing about quite a few of the people who graduated along with me from my mediocre uni.
