As part of my property work, I have recently needed to research the law relating to trees. A small registered company owned by residents of a “country house development” of about 15 properties has extensive grounds which are laid out to parkland. The directors were concerned as to the company's potential liabilities. The answer was not immediately obvious.
The case of Whitley Parish Council v Cavanagh (2017) EWHC 278 QB is what you need to look at. I advised as to the extent of the necessary immediate work required and as to a proper system of review of all the remaining trees, with a pro-active regime for individual trees that could be identified as deserving of regular inspections. I am confident that the new system will demonstrate an appropriate and proportionate approach to the management of the parkland.
If you need a tag to identify the extent of the duty, try "the measured duty of care" and perhaps have a look at the case of Vernon Knight Associates v Cornwall Co Ccl (2013) EWCA Civ 950.