The 120p a share bid, which values Lopex at about pounds 67 million, represents a 39 per cent premium over the all-share offer made by Incepta on July 1.
Analysts pointed out that even if it lost out to Havas Incepta would walk away with a pounds 12 million profit on the Lopex shares it has already bought at between 30p and 40p each.
Havas has irrevocable undertakings from investors representing 20.7 per cent of the issued shares, plus another 3.5 per cent held by Lopex directors.
Lopex chief executive Mr Peter Thomas said Incepta's offer had flushed out ten other interested parties, but Havas was able to move quickly as it had previously run a ruler over the company.
Mr Thomas, who owns two per cent of Lopex, said any counter offer from Incepta would have to offer a cash element to be attractive.
The all-share bid came a day after rumours caused Lopex shares to rise sharply on the stock market.
Incepta chief executive, Mr David Wright, said he had hoped to announce a recommended offer next week after meeting Lopex directors on Monday.
Lopex is slightly smaller than Incepta, employs just under 900 people, and has a comprehensive regional network of offices including Birmingham - where its Grayling public relations subsidiary has an operation.
Analysts, however, have cut their profit forecasts for Lopex, reducing estimates from pounds 7.1 million in April to pounds 6.3 million.
"Lopex has been standing still for some time and has clearly underperformed.
"This is a full, fair offer at a substantial premium to Lopex's share price before the news leaked out.
Incepta is offering nine new shares for every four Lopex shares, valuing each Lopex share at 86.6 pence.