The Fuzzy Furry
Old Timer
If you want to stay there, buy some electric fencing, and fence the field/part of it yourself. Your electric fencing means it's yours to take with you when you leave, you could do a smaller bit with one other pony as companion to yours if you worked that out with the other liveries, and with a decent energiser/battery, you won't have escapee pony problems. I've done that in the past to stop ponies eating fencing but also where the fencing is a tad wobbly, and it's worked really well.
This ^ so perhaps try to do this, or entertain moving elsewhere where the fencing will keep your animals in.
It IS a landowners responsibility to prevent stock from straying from their land and if this is not prevented, then the LO is liable for any damages.
This does not take into account how poor any fencing is, neither do horses come under 'livestock' BUT he can still be accountable for damages caused, though you should also make sure your equine IS insured for 3rd party liability (such as being a gold member of the BHS which would cover you)