I wouldnt suggest a cleansing routine,i would suggest benzol perocide to help you rid the active stuff,panoxyl.just applybit to the effected areas.

whats more inportant is knowing what is aggravating your skin,acne cant be stopped or cured with a tablet but you can control it!

so what i would suggest might seem tough but before i start remember you got a routine already,its life and day by day.

wash with warm clean water,not hot,warm,always use a clean dry towel each time and pat yoyr skin dry.

apply a moisturiser thats goid for your skin,i use simple brand,its called simple.

so apply moisturiser after washing.but also apply some panoxyl ir whatever topical you chose to control and rid the active stuff,it will help by reducung the inflammation.

cut out all sugary stuff,none at all,no bickies etc etc.

eat sweet potato not white,eat wholemeal bread not white or other brown whole bread,limit your consumption to say max 4-5 slices daily,if you can try gluten free.eat loads of veggies,carrots,cauli (you know the score on this) try not to glut too much on meat,eat it but dont eat tons of it,try to stay away from fried food and mashed or blended stuff,no smoothies.

drink few glass's water a day,keep your hygene good,dont finger your face and wash hands regular.

get sleep every day and stay stress free and try not to masturbate too often,i am trying the masturbation bit myself to see if it works and reduces breakouts.

keep the routine,dont break it and after it starts kicking in you should see difference (fingers crossed) 

keep on on skin when you change routine and know what your eating,its important so if you breakout you can see the correlation between what you had to eat and your skin,if you suspect something you ate made you react you can eliminate it from your diet and substitute something else instead.

eat a couple of pieces of fruit a day but try to stay away from citric based fruit to start off with.

come back and update your progress but dont rely on just topicals,they can spoil your skin and you become dependant on them,its better to manage and try to keep your skin healthy.

A retinol product will clear congestion out really well. I currently use Epiduo Forte. I know you said no medications, but at some point you're going to have to bite the bullet if nothing is working. Epiduo is a combination of retinol and benzoyl peroxide. It fights acne bacteria and dissolves sebum plugs at the same time. I've been using Epiduo for a little over three months now and I have no clogged pores at all. I used to have very oily skin that would cause build up literally overnight. Now my pores are empty.

Don't use harsh face washes, being overly aggressive is going to flare up and aggravate your face. I stay away from all those acne washes at the drug store, I've found they do not work. For my face I alternate between plain white Dove soap bar, and an antiseptic wash (like Hibiclens) you can find the antiseptic wash at any drug store in the first aid section. I use the wash when I have active acne and need to keep the skin free of bacteria.

For moisturizing, to help heal PIH and cystic scarring, I use vitamin E oil, I get mine from Trader Joe's. Not sure if there are any TJ's in the UK but you can probably find the oil on Amazon. Vitamin E oil works really well in preventing acne from forming in the first place, it doesn't clog pores, and it works really well if you are a dermaroller or dermastamp user.

At least once a week you should be using some sort of clay or mud face mask to draw impurities out. My personal favorite is Borghese Fango Active Mud mask.

https://www.amazon.com/Borghese-Fango-Active-Face-Body/dp/B00554AHTU?th=1

https://www.amazon.com/Trader-Joes-Vitamin-Oil-Pack/dp/B00TX998OS?th=1

https://www.amazon.com/Dove-Beauty-Bar-White/dp/B0016G2BJK

https://www.epiduoforte.com/about-epiduo-forte

http://www.hibiclens.com/