After closing all but one of its parks, all eight were open again by late afternoon.
A Royal Parks spokesman said: "Staff and contractors have worked hard to open the parks as quickly as possible and keep disruption to a minimum.
"Our initial estimate is that we have lost around 50 trees from across the Royal Parks, from a total of around 130,000. We will have a clearer picture when we have carried out a full assessment, which could take a few days.
"Tree works will continue over the coming days and damage may result in further trees being felled for safety reasons."
The work was carried out by existing contractors.