The three-way pitch, handled by COI, also included Mother London and Rainey Kelly Campbell Roalfe/Y&R, which created an outdoor campaign last year warning of the on-the-spot penalties for drunkenness.
A spokesman for the Home Office said: "We have shortlisted one agency, but no decision has been made as yet."
The Home Office and the Department of Health, which are heading the campaign, are understood to be in the final stages of negotiations with the agency.
United's integrated campaign will cover cinema, satellite TV, radio, ambient and online.
The campaign, expected to launch in the autumn, follows the liberalisation of licensing laws in November last year. The new laws allow pubs and bars to stay open longer. The move has been criticised as encouraging binge-drinking.
COI called the pitch in November, but the review was delayed until March after officials imposed a freeze on public-health funding.
Opinion, page 21.