I made some guesses and added your profile to The Ordinary!
. They actually have suggested a Squalane cleanser rather than a BHA one. Might be good - DS uses that one and it does seem to be nice. This is what I'd suggest:
Evening: cleanse using the Ordinary Squalane cleanser OR if you're already doing a cloth cleanser, use that (do you use a balm or something with your hot cloth? M&S does a few options for balm cleansers and people on here rave about the ELEMIS (v expensive though) one. The Body Shop also does a cheap and cheerful camomile one which is actually very nice).
Online, this sort of red bumpiness gets lots of hits for Azelic Acid - so perhaps try one from The Ordinary or Inkey list as an evening serum.
Then a moisteriser - personally, I don't rate the Superdrug range. I've tried a few of them and they're just not great. For evening, I think a good option is the Neutrogena moisterisers - I use the super hydrating one it's very light though, sort of gel like so I like it and it doesn't make my skin feel at all oily - I accidentally bought the regular moisteriser from this range recently and actually, have been using that at night instead and it's been fine too. Another one you might like is the Sali Hughes by Revolution options - she's got a couple of good options that are all quite light I think. [Actually - I just looked at the website link above, it might be worth having a little look round her website as it's quite good at explaining ingredients etc]
Then in the morning, I would just splash your face with water. Then a light vitamin C serum - I just remembered that Sali Hughes also does an intro one. I've never tried it because I'm up to the pretty much highest level of vitamin C possible and I think hers is much lighter, but it might be a good intro option for you. Then a good moisteriser on top, with SPF. As I said, I use the Elf Hydro Boost but any high street option would be good. If you don't want to buy all new at this point, perhaps stick withy our existing Super drug one for a while.
I would expect it to take a couple of weeks to see a real difference, but if it's right for you, you might see very subtle improvements after a few days. Nothing huge, but more in how you feel.