I feel like I have seen plenty of tourists eating there (and always felt sorry for them).
Rather than money laundering or anything shady like that, I always assumed it was just a fiendishly well-designed tourist trap. The branding is perfectly pitched to make it somehow look both classy and cheap (which are exactly the two things you want and need as a tourist in London).
I went there with family in the 80s as a kid. They weren't that bad, but you have to remember the standard of dining in the 70/80s uk was pretty terrible at that point. There were lots of people there and not much choice. At this point McDonalds was a new and cool thing in the UK and it was many years before things like Weatherspoons came and brought cheap, low quality dining/drinking to the city masses. I remember at that time chains were seen as being quite cool and fancy and the choices were bad pubs full of old men that didn't allow children, fish and chips or breakfast places.
Rather than money laundering or anything shady like that, I always assumed it was just a fiendishly well-designed tourist trap. The branding is perfectly pitched to make it somehow look both classy and cheap (which are exactly the two things you want and need as a tourist in London).