Not possible. If you do A-Level Maths, the second A-Level must be in Further Maths. Pure Maths contains two 'pure' units on top of the 'core units' you take in the standard A-Level. Thus, the difference between pure mathematics and mathematics is that you take 'pure' and 'core' units in the first, and 'applied' and 'core' units in the second.
However, once you have one of these, a second A-level must be in 'Further Maths', where you do all of the 'pure' units (more than in 'pure mathematics') and make up the remaining units out of applied stuff.
I know this because I have Maths and Further Maths at A-Level.