What would you say I should aim for with these AS grades?

You can get into chemical engineering but maybe not a russel group with grades like ABB.

You've got an A dont waste precious time resitting, do an alevel maths you'll probably get an A aswell. and than do ONE of physics/Bio and the reduced work load should get you an A.

you could always apply for the bachelors degree and then transfer onto the masters after your first year?

Your AS grades (other than Biology) are decent - i.e. they will be looking at the predictions, in terms of whether it's worth giving you an offer. They recognise your AS grades aren't final.

I got BBBc and got given an AAB offer easily enough for a course, so you don't have to have the exact grades at AS - just make sure the predictions are realistic. If you e-mailed them they would probably say based on grades they wouldn't rule you out, but ultimately an offer will depend on everything in combination.

Edit:
With regards to BSc vs MEng:
Many courses have the same requirements now, so you may as well apply for MEng. If the BEng is lower and you realistically don't think you'll make the grades for MEng then apply to that. In your case, I don't think that's true, and they'd probably prefer to take you onto the MEng and switch you to a BEng later if necessary.

You are still one student in the year intake, whether it's BEng or MEng so it doesn't affect your chances of getting in. If they feel you're not suitable for the MEng they can also make you an offer for the BEng from your original application.

Funding isn't too bad, but agreed it all tends to be easier to go from MEng to BEng rather than the other way, but it's quite common so it does get sorted out easily enough. The main thing about swapping up is that you ought to be achieving at least a 2.1 usually (varies by department, however).

My GCSEs:

4A*s, 5As and 3Bs.

My AS Levels:

A - Full A Level in Pure Mathematics
B - Physics
B - Chemistry
D -Biology

I've dropped Biology.

Predicted grades:

A* - Pure Mathematics if I resat the exams
A - Further Mathematics
A - Chemistry
A - Physics

I would prefer to go to a RG university since they looks nice. Should I am for a Bachelor's degree with my grades? I'd really like to do a Masters though. I'm also thinking of doing something like Chemical Engineering. Should I just throw all my hope out the window? I read a thread about another person in a pretty similar position as me and he's aiming for a BSci, so now I'm worried that I've been thinking too high.

I don't think I'll drop either Physics or Chemistry since I've already dropped Biology. Do you think I should call universities to ask if they'd consider me? Or would they just give generic responses like "we'd need to consider your personal statement as well"?

I've been thinking of going to Scottish universities like Strathclyde, Aberdeen and Heriot Watt where requirements are like AAA-BBB, but applying to somewhere like Heriot Watt for mechanical engineering seems like a waste of my A in Maths. Plus, I'm not really interested in mechanical engineering, but it'll probably land me a job early on.

Aim for some high ones such as bath (aaa), ucl (a*aa), Manchester (aaa), Nottingham (aaa), Sheffield (aaa), Birmingham (a*aa), Edinburgh (aaa), leeds (a*aa)
Some middle ones such as Loughborough (AAB), Newcastle (AAB), strathclyde (AAB), Surrey (AAB), Swansea (AAB)
And some insurance ones such as teeside (280 ucas), Bradford (280 ucas), Chester (bcc), Huddersfield (300 ucas), hull (300 ucas) , Lancaster (abb)
I would opt for one high, three Middle and one low.

youve got an A in further maths and you should get an A in normal maths. and aim for a B in your other 2 than, its risky that youre doing 3A2+AS without even retakes but you should try and get AAB-ABB relistically scottish unis should take you, and with AAB you can get into some russel groups, apply to a mix of both but stay away from the top end ones is my personal opinion maybe apply to one or 2 and have it as your firm if you want to be risky but im not sure to recommend/not recommend that to you.

Sorry, I should just clarify that I've got an A in my full Pure Maths. I am only studying Further Maths now and haven't taken any exams for it. I only have ABBD. Thanks for your advice though, I'll see which ones of the top end universities would be easier to get into.

I would prefer to go to a RG university since they looks nice

You can't have pure maths and further maths together; both qualifications use FP1 and FP2 and you can't use a unit twice.

Repped you because this sentence had me in stitches.

But yeah dude your predicted grades are fine, go for it. Also you don't need to worry about whether or not to do a masters for another 3 years, one step at a time my friend!