You make a legitimate purchase from a legitimate company. You are then asked if you want to save £15 on your next purchase. When you say yes, Shoppers Discount grabs your details (including, we think, credit card details on a passthrough from the legitimate company). You agree to the t&c, which you probably didn't read, which make it clear that you'll be charged £10/month after the first 30 days. They do email you, repeatedly, but you're probably filtering out their emails. You don't realise it's not the original company until after you've signed up.
Legitimate companies include Pizza Hut, The Trainline, and Interflora.
The good news in all of this is that *I* didn't get caught out, it was malwen, and I *did* check my card assiduously enough to spot it on the very first month. So I feel nice and smug now. And they quickly and efficiently refund your money when you complain (they are clearly making plenty on the people who never notice), so we haven't lost even £10.
But honestly. How is this legal?