Dimmock, who is fronting the campaign, said: "Enforcement - that is where I can see problems. The best way to go is trying to educate people about their plants and how to dispose of them. There is a lot of public ignorance."
The Government is running risk assessments to take the more decisive step of banning plants, but that process is still ongoing.
Risk assessments costing £2,000 each on dozens of plants, including non-pond plants, has no set date for a conclusion. But Defra officials said some of the plants being assessed will be banned - joining Japanese knotweed and giant hogweed on the outlawed list.
Some online retailers are still selling floating pennywort, New Zealand pigmyweed, water primrose, parrot's feather and water fern. But they are now to be banned from being planted in the wild and likely to go completely when Defra completes its risk assessments.
Plant Life invasive plants officer Sophie Thomas said the charity supported risk assessments but would like more plants to be added to the list. She said the timing of the Government campaign had "not slotted together that well" with the banning of nine plants from being dumped in the wild in April.
Plant Life's primary concern was for the preservation of wild plants. Thomas added that limited bans such as dumping plants in the wild but not on selling invasives were "very difficult" because of natural dispersion of garden and amenity plants by, for instance, birds.
"We would like many to be banned," she said. "We're worried that parrot feather is still widely available. Awareness is quite low."
Thomas said many invasives have origins in ornamentals and aquatics and there is "no avoiding that". She added that Defra must strike a "balance between ecology and the impact on trade".
Defra minister Huw Irranca-Davies said he favoured the hearts and minds approach: "Even if we ban certain species they are already out there in the wild." The HTA, Ornamental Aquatic Trade Association, RHS and Plant Life are all supporting the campaign.