Abbott Mead Vickers BBDO and Grey London follow closely behind with four campaigns on the list, while Ogilvy & Mather, Karmarama, J Walter Thompson London and VCCP have two nominations each.
Adam & Eve/DDB is shortlisted for John Lewis and John Lewis Insurance, alongside the retailer’s media agency, Manning Gottlieb OMD.
The Omnicom agency is also listed for Save the Children, Volkswagen and Wall’s.
AMV BDDO is on the shortlist four times for its work for Guinness, Pepsi Max, Sainsbury's and Snickers.
Ogilvy & Mather has two entries on the shortlist, for Dove and the Government; while Karmarama is shortlisted twice for Plusnet and Costa. VCCP was also shortlisted twice for its work on Coors Light and Macmillan Cancer Support, while JWT London was nominated for Kenco and First Direct.
There were four international entries on the shortlist: two from Australia (Narellan Pools by Affinity; Officeworks by AJF Partnership and Initiative); one from New Zealand (New Zealand Transport Agency by Clemenger BBDO Wellington); and one from Denmark (Spies Travels by Robert/Boisen & Likeminded).
The 2016 Awards are partnered with Campaign, Hall & Partners, IPSOS, Newsworks, OutSmart, Radiocentre, Thinkbox and Warc, and sponsored by Marsh.
The winners will be celebrated at a black-tie gala ceremony at the Hilton Bankside in London on Wednesday 2 November.
Dame Dianne Thompson, the chairman of judges and former chief executive of Camelot, said: "The 39 shortlisted campaigns provide absolute proof that marketing improves a business’ bottom line.
"For anyone looking at how creative ideas can be turned into commercial success, look no further than these exemplary cases. Congratulations to all those who have made it onto this prestigious list."