Broadway, formerly part of Interpublic, is attempting to invoke Transfer of Undertakings Protection of Employment regulations to force DLKW to take on the 25 to 30 members of staff who worked on the business.
TUPE regulations were introduced by the Government to provide protection for any group of employees when a large contract shifts from their employer to another company. Invoking TUPE ensures the group of workers' ongoing employment on that business, also providing them with rights to the same terms and conditions.
Traditionally, this has been applied to call centre or administration businesses rather than to high-end business specialists.
However, if Broadway succeeds then it would avoid having to make redundancy payouts to any of its staff.
DLKW won the £10 million Vauxhall dealership account in May this year following a lengthy pitch against the incumbent and a number of other small agencies.
The Vauxhall business was one of Broadway's flagship accounts, alongside HSBC, which it also lost earlier this year. Its client list includes BSH Home Appliances and COI Communications.
In 2002, DLKW scooped the £15 million Vauxhall retail account from Broadway. DLKW also works on the Corsa, Meriva, Astra and Agila brands.
Vauxhall, DLKW and Broadway, all of which have lawyers acting on their behalf, declined to comment on the story.