The Government's principal plant health and seeds inspector Dr David Slawson will shortly be on secondment with the charity, which is aiming to draw up biosecurity protocols for the gardens.
The trust's lead adviser on Phytophthora, Ian Wright, told the IPPS conference: "None of us wants to restrict trade but we need to reduce the risk of introducing pests and diseases into the country.
"It's not a case of putting lots of inspectors at ports. It involves us also taking responsibility and having biosecurity on our sites."
Wright continued: "Garden managers need to talk to growers. One affects the other."
If the Government chooses the stronger contain-and-eradicate measure, proposed in the Defra consultation on the disease, "we can't allow it to be reintroduced from other countries after we've spent money on a clearing operation", he added.
Wright said the National Trust could not accept the minimal management option, proposed in Defra's consultation on the disease, because of the risk to native plants. But he also said that the charity is uneasy about the timing of the destruction of disease hosts under the stricter second option.
"We need the time to propagate rare and important plants before they are destroyed. Imagine a Cornish spring garden cleared of every Rhododendron - there would not be a lot of plants left."