The London sank off Southend-on-Sea, Essex, after an explosion in 1665.
A charitable trust has been set up to preserve the "unique" wreck and the artefacts found on board.
Trustee Steve Ellis said in the past 12 months, ships heading to the London Gateway development had affected the wreck "more than ever before".
"The wreck is deteriorating rapidly, we're noticing it on a weekly basis. We're trying to recover as much as we can," he said.
"You wouldn't let a site like this on land deteriorate like it is, so we formed a trust to try to protect it."
The ship sank on its way to fight the Dutch, killing about 300 crew.
The wreckage of The London was only discovered because of dredging works during construction of the port's shipping channels in 2005.
Southend Borough Councillor Georgina Phillips said she would like to form a "positive relationship" with DP World, the company that operates London Gateway.
"We're hoping to build the relationship to the point where they might donate towards the wreck," she said.
"If we can't get the big container ships stopped, the company might be able to help in another way and make something positive out of it."
Mr Ellis, a licensed diver, said the quality of finds from the wreckage had so far been "absolutely outstanding", and the trust had been formed to protect, preserve and eventually display the items.
Cargo ships sailing near the site of a historically significant shipwreck have caused its condition to deteriorate rapidly in the last year, divers say.