If I get someone to clean my gutters (by sliding down the roof untethered) who is liable if there is an accident? The householder or the handyman (let's assume he doesn't have any insurance).
Depends. If he assured you it was safe to do so, and he fell because of his own negligence, he is liable.
If he fell because of loose slates, guttering or other poorly maintained thing you failed to mention, you are.
To avoid any issues, show him the required job then ensure he chooses the method by which the job is done. Tools and equipment should be provided by the handyman, not you.
The 'liability to third-parties' aspect of your buildings' insurance will then give you cover in the event of accident.
Thanks for the answers folks. Stewie, he needs to get on the roof as I live 3 up. He's done a few of the neighbour's gutters but went up on the roof rather than a cherry picker.