The St Jude storm on 28 October forced more than 25 National Trust properties in the South East as well as Kew and other gardens to close. Erena Wilson died at Kew in September 2012 after being struck by a falling branch and an inquest is ongoing.
"Everyone has to be more careful," said Curtis-Machin. "We're talking about hundreds of thousands of pounds of legal bills and the knock-on PR effect. People are being more cautious because of the litigation culture. When people pay for entry they have high expectations. If something goes badly wrong, they are tempted to seek redress."
A Kew press officer said: "It is standard practice to close in high winds." Kew lost 10-15 young and mature trees in last month's storm.
Garden consultant Alan Sargent said: "After the Kew death we will never go back to the old days when you took your chances. That one Kew death transformed everything, not just because of insurance but we now need to understand that every tree is dangerous.
"There's so much leaf on trees the gardens had no choice but to close. The ground is so wet trees fell like ninepins. There's a catch 22 - if you don't inspect your trees you're dead and if you do you get a report that you have to act on. Owners of trees aren't to be envied. They're a big responsibility."
National Trust gardens press officer Jeanette Heard said: "We have a moral and legal duty to ensure that the public and our staff are not exposed to risks as far as is reasonable and practicable. Litigation affects our reputation, so if there is any risk you need to close."
She said property managers decide locally what to do: "It's on their heads. You have to be really careful and on that basis they are more cautious in mind with not wanting litigation."
A Royal Parks representative explained that senior management shut down parks after considering the risk of damage to trees, as well as the implications for public and employee safety, taking into account factors such as wind speeds, tree leaf and ground conditions.
Gristwood & Toms manages trees for two areas that saw fatalities from falling trees during the storm, Watford and Hounslow.
Director Andy Toms said: "Our guys had to be at the Watford case when he was cut out of the car - it wasn't good. We had 2,000-3,000 calls to deal with and when you deal with one job you find five more.
"We know which staff are suited to which tasks. You concentrate your skilled climbers on the awkward jobs. The problem can be where the local authority wants to clear it themselves."
London Tree Officers Association vice-chair Richard Edwards said: "Tree officers and contractors coped well."