Which is the correct preposition?

I would say "on" Farrer Road, but I'm not familiar with the British way of saying this.

Could a BE native speaker please comment? Thanks.

On.

Do you ask the same questions over and over and over again until you get an answer that pleases you?

https://dictionary.cambridge.org/grammar/british-grammar/at-on-and-in-place

Somewhat ironically:

Heaven forfend Miss Toad, was that sardonic outburst a peremptory, pejorative prerogative?

One would be inclined to say 'The Rolls carked it on Farrer Road' certainly not 'at Farrer Road' although one might admit 'in Farrer Road'.