Produced in both a liquid and a thickened version, most famously by Goodall, Blackhouse and Co, established in Leeds in the 1830's, and later by 'Goodalls of Ireland' at Tallagh ouside Dublin, where they still manufacture both versions.
During the 1840s(?) Goodall's supplied tiny 4 1/2" saucers in the popular 'Willow Pattern' style with advertising slogans, presumably intended to sit under your bottle of YR and collect any drips.
Yorkshire Relish 'Willow Pattern' plate
Image: https://www.premierantiques.co.uk
Yorkshire Relish is now relatively rare in England, but has a continuing popularity in Ireland where it is produced under the 'YR' brand by Robert Roberts.
Other English piquant liquid sauces include:
Harvey Sauce
Worcester Sauce
Mrs. Comber's Sauce
Wow-Wow Sauce
Muckleston's Celebrated Shropshire Sauce
Reading Sauce
Yorkshire Relish