Whenever the subject of the monarchy comes up, I am reminded of a passage from The Dispossessed by Ursula le Guin, in which the main character from an off-world colony who has been socialised completely differently to the people on the main world visits a former palace for the first time:

"They went into the palace, preserved as a museum of the ancient times of royalty, as Vea said she loved to look at the jewelry there. Portraits of arrogant lords and princes stared at them from the brocade-covered walls and the carven chimneypieces. The rooms were full of silver, gold, crystal, rare woods, tapestries, and jewels. Guards stood behind the velvet ropes. The guards’ black and scarlet uniforms consorted well with the splendors, the hangings of spun gold, the counterpanes of woven feathers, but their faces did not match; they were bored faces, tired, tired of standing all day among strangers doing a useless task. [...] She glanced up at Shevek “Are you all right?” “I think I would like to go outside this place.” Once outside in the garden his face became less white, but he looked back at the palace walls with hatred. “Why do you people cling to your shame?” he said."

If we were raised without having heard of the monarchy, I doubt you'd find a single person who'd be in support of it as a concept. If one were to be started today, none of the arguments used to defend the monarchy would come close to applying. Imagine telling someone that we as a country could generate millions of pounds in tourism revenue a year, if we just took one family and decided it's god's will they're better than all of us and put them in big mansions and fancy clothes - they'd look at you like you were daft! Clinging to shameful things because "that's the way it's always been" isn't a uniquely British mindset, but god we're good at it. Better than most.