I applied for Chem Eng via NatSci and got an offer this year.
If you're applying for Chem Eng/Petroleum Eng everywhere else, your personal statement will be mostly Chem Eng based.
What you have to remember is that the basis of Chemical Engineering lies in the sciences, so talk about your interest in science and how that relates to engineering. For example, maybe talk about what in Chemistry interests you and it could co-incidently be somethign that is very relevent in Chem Eng today!
The NatScis know that you're applying for Chem Eng via Natural Sciences, so will expect you to have a very Chem Eng related PS - don't worry about it
As long as you apply for CHemical Engineering Via Natural Sciences on UCAS, They will be very understanding - use your SAQ from Cambridge to talk more about Natural Sciences specifically.
I would stress though that you should really be talking a lot about what interests you in your A level subjects and how you feel that you could put it to good use at university.
UCAS has really good tips on what to include for your personal statement.
Also, I wouldn't mention anything specifically for Petroleum Engineering, except maybe that you have an interest in Petroleum (but mention it as an offshoot pf Chemical Engineering).
To be honest, if I was just applying for Chem Eng courses, I would have still mentioned a lot about the sciences because they're what really links your A levels to degree level.
(sorry if this isnt making too much sense, it's 4 am where I am right now... Inbox me if you need any more help