This made the UK the second most nominated country in the category, just behind Germany, which has been shortlisted 22 times.
Among the UK agencies nominated for the Design Lions are Abbott Mead Vickers BBDO, which made it on to the shortlist with its work for the Museum of Childhood.
CHI & Partners was also among the nominees, for its "X Factor" campaign for the Carphone Warehouse.
JWT London was nominated for its "Wimbledon grass art" work for HSBC, while McCann Erickson made it on to the shortlist for its own agency branding.
The most-nominated UK design agencies were The Chase Creative Consultants and Williams Murray Hamm London, which both picked up three nominations each.
The Partners, which won a gold Design Lion last year for its "grand tour" campaign for the National Gallery, has picked up two nominations this time around, for its work for Mr Singh's Bangras and the children's hospice charity Richard House.
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