Dangerous overgrown trees overhanging our garden

Trees behind our garden are overhanging with dangerous heavy branches posing a risk to my children playing. Frequently branches fall that are large due to birds nesting. Hygiene concern as continuous pigeon and bird poo covering the garden and has landed on children. Needs to be cleaned daily before they can play. Ivy is intertwining into our new fence now too. Tree simply too high to be reached to resolve. Overhanging our property by 3-4m. Please can this be cut back to a manageable size that does not overhang as much? Happy for this to be accessed via our property if contacted.