Do you know what exam board he is doing? Ds did OCR (not MEI) and used the standard OCR textbooks which seemed fine. You buy the ones applicable to the modules he is doing. The books seem to cover either one or two modules (eg: Core 1&2, core 3&4, M1, M2&3, FP1, FP2&3 etc). I imagine having already done highers he will find the maths modules quite straightforward and probably some of the f. maths modules too.
The other books I rate are the ones I used eons ago for my maths A level by Bostock and Chandler. The very old ones I have are called Pure maths 1, Applied maths 1, Pure maths 2 and applied maths 2, where the '1' books covered maths A level and the '2' books covered further maths. Things have changed a bit with the new syllabuses though so the divide isn't as clear cut and there are more recent editions than the ones I have (I've seen one entitled 'core mathematics'), which are still well regarded but are still old enough not to reflect the latest syllabuses so you'd have to pick and choose the right chapters for each module carefully). The books still cover all the topics and have good exercises but probably the books that relate to the actual syllabus are easier to use.
For UKMT/BMO go to their website and order past papers and practice those. They may have some books that are useful too, I think there was a recent one specifically aimed at BMO preparation.
Also join the forums on nrich and tsr, both good for advice and help when stuck.
For STEP there's an online book by someone called Siklos which is 'the' text for STEP, but the key is lots and lots of past paper practice. TSR is also good for support and help with STEP too.