From a customer point of view, "Which?" magazine started recommending to buy rather than rent a colour TV in the mid-late '70s, saying that buying was cheaper than renting in the long term.
Nonetheless, many people kept renting, perhaps because they always had done, perhaps they liked the reassurance of free repairs and a free loan set if theirs broke down, or the flexibilty to change their set for a newer model. Perhaps they didn't have the cash to buy a new TV outright. Borrowing money wasn't so easy or cheap. You had to see your bank manager, or sign an expensive HP agreement.
When video recorders appeared, lots of them were rented. Just like the first colour TVs, they were expensive and often unreliable. There was also some doubt over which of the 3 competing formats would 'win' out of VHS, Beta and Video 2000. Customers were scared about buying something expensive that could quickly become obsolete. It made sense to rent.
By the late 1980s, the argument over which video format to choose had been well and truly settled. But there were other factors. Retailers started offering instant credit - buy now, pay later. I guess credit restrictions were eased in order to start the "borrow, spend, consume" cycle which is supposed to boost the economy.
Even the big rental companies must have seen the writing on the wall by the late 1980s. Radio Rentals for a long time refused to sell TV sets for fear of harming their profitable rental business, but by the late '80s lots of ex Radio Rentals TVs and video recorders started turning up in secondhand shops as they sold them off cheaply. It was often possible for a customer to buy an ex-rental TV with a few months guarantee for less than the deposit on a new rental. It no longer made sense for the customer to rent.
I'd agree with Till that TV rental started dying in the late 1980s if not before. Despite that, High Street TV rental shops continued into the early 2000s. Granada and Radio Rentals became boxclever, who were eventually bought by a company called BrightHouse. They offer large items like TVs and furniture on weekly payments, a bit like rental and no doubt aimed at the poor who might traditionally have rented a TV. Ironically it's a very expensive way of buying.
In the final twist to the tale, BrightHouse acquired the "Baird" brand name from the former Radio Rentals shops they took over. You can now find a range of Baird LCD TVs in their shops. No relation to Thorn of course.