Trees overhanging boundaries of private business

I'm the Business Manager of the Dorchester branch of McDonalds (Lewco Holdings LTD). As you can see from the photos, the trees located in the land to the east of our property overhang across the boundary.

The concern I have regards the high potential of falling branches causing damage to the vehicles of both staff and customers. The relative isolation of the store means that it is usually quite windy in the area which increase the risk of falling branches.

The carpark does have CCTV which will be able to identify any potential damage caused, but ideally I'd like to prevent its occurrence in the first place. I'm requesting that the owners of this land undertake works to cut back the vegetation overgrowth.

I logged this on FixMyStreet earlier, however it directed it to the Dorset Council. They have told me this land is managed by National Highways