To my knowledge there are no rules against it, it is just a major and expensive plumbing project requiring redoing the whole kitchen. And so as a landlord why bother, you will always find someone willing to rent, no matter how unlivable the place. This dynamic was hardly unique to the Barbican, it was the reality of being a tenant in London, and ultimately one of the reasons I left. London's housing stock is just terrible compared to every other city I've lived in.
In my last apartment, I installed a tabletop dishwasher on the balcony and had it share the water inlet with the washing machine using a y splitter.
It would probably be an eyesore and a huge space killer to use indoor on the kitchentop but thought I'd share a non-invasive solution I used.
The size of the dishwasher was decent, and with some tiny concessions around placement it was perfectly fine for daily washing although I generally prefer to wash pots and pans by hand regardless of dishwasher space fwiw
I’ve lived in 4 different flats in the Barbican and they all had a dishwasher. I think only the studios you’d have a problem finding space for one. Of course in the others it is a preference whether you want to lose space for other things or not. It is not a lot of extra plumbing. It is usually when they want to preserve the original kitchen (or a cheap landlord as you suggest - although all the ones I had there were great)
