The number dwarfs the previous year's promotions, when just two associates were made up.
BLP managing partner Neville Eisenberg said: "The number of promotions is in line with our continuing growth, which is being driven to a significant degree by the fact that our clients are involving us in a greater number of larger, more complex transactions."
The firm had its previous biggest promotion round in 2004-05 with nine new partners, while six made the move up in 2003-04.
Five of the 13 promotions in the current round are female, and the firm now boasts a total partnership of 167.
"[Five female promotions] reflects the success of our diversity programme in the firm," said Eisenberg.
The promotion spree has seen a return to favour for real estate associates, with three general real estate promotions and one each in construction, property finance and real estate litigation.
The firm's corporate practice has benefited from three promotions, while there were two in finance and one in tax.
In the past three years, lateral hires were nearly double the number of internal promotions, with 28 laterals compared with 17 promotions since 2003-04.