The group argues tobacco firms will switch marketing spend on tobacco brands to non-tobacco products bearing the same brand names to retain a marketing presence.
It suggests the firms should be allowed to spend no more than 5% of the revenues from non-tobacco products on marketing them in any 12-month period. ASH also recommends that brand logos on non-tobacco products should be distinct from the logos of the tobacco brands themselves.
"The government needs to ensure that all possible loopholes are closed, otherwise any ban is going to be limited in its impact,
said ASH director Clive Bates.
There is now speculation that the ad ban could be further delayed because the government has notified the European Commission of the details of its legislation.
The legislation may not be ready in time for inclusion in the Queen's Speech.