Early on, when I thought I had a gluten allergy, I created a "free from" blog. You can find the link at the bottom. The idea was to provide a guide to where to find Free From foods in different British stores eg go to the farthest corner, turn 180 degrees and it will be facing you (that was generally the best principle). It's still there but nobody ever contributed to it so it has never been developed or used.
I am tempted to try the same for salicylate free shampoos and conditioners - except there would be hardly any entries. Somebody suggested getting baby shampoos - but they smell awful.
The best on offer recently has been a "derma" shower gel, which I have been using. My hair is starting to stick up like a punk. So I had another search today. Lloyd's chemists - nothing. Back to Tesco. They are definitely no longer selling the wheatgerm and cornflour range. I picked up a Head and Shoulders conditioner "for sensitive skin". I will let you know.