He was the son of William Beilby, a jeweller and goldsmith of Durham who later moved to Newcastle upon Tyne to look for better opportunities. Ralph became a silversmith, jeweller, and seal-engraver under his father and elder brothers Richard and William junior.
In 1767 Thomas Bewick was apprenticed to him.
In addition, he became a copper engraver to meet the demand of the then North England market. His plate "Thornton"s Monument" in John Brand"s History of Newcastle shows his craftsmanship in that field They became partners 10 years later.
The texts in Bewick"s A General History of Quadrupeds (1790) and History of British Birds: Land Birds (1797) were drafted by Beilby and revised by Bewick.
According to Bewick"s account, Beilby wanted to have his name appeared in Land Birds as the sole author However, upon Bewick"s disagreement, neither of them was named as the author
The partnership came to an end in 1797, after the publication of Land Birds. They were tentatively reconciled in 1800, co-operating again for some projects, including the publication of Figures of British Land Birds.
Bewick came to Beilby"s defense when the latter had been defamed in a supplement to the third edition of the Encyclopædia Britannica published in 1801.
