Legally yes, it is the owner's responsibility to keep their dog on their property (as is true for most other animals but not cats) unless you have a specific obligation in your deeds - sometimes property can be sold by farmers with the obligation to maintain stock-proof fencing being transferred.
Assuming that you don't have such an obligation, then even though the hedge that was removed belonged to you, you are not required to put any fence back if you chose not to. In practical terms, it will be years before a beech hedge is inherently dog proof, so they need to take measures themselves appropriate to their dogs - as Mark points out, different dogs need different levels of control to keep them in. One of mine can jump over a 5 foot fence without breaking his stride, if he wants to. Our fences are 2m high to keep him in, but he doesn't dig and he's too big to fit through the holes. Our neighbour's terrier can get through teeny gaps to turn up outside my door. I just keep taking him back. They know the risk they are taking by not keeping him in - in the end it's your neighbour's dogs' safety that is in question. Around here (farming country) an unaccompanied dog is very likely to be shot. Where you are it may be different - perhaps getting run over on the road is more of a threat. so keep telling them - take the dogs back, phone them and ask them to come and get the dogs but keep going on until they do something. Don't get into a discussion about whose fence it is, just keep pointing out when the dogs escape.
If you can't get anywhere by talking to them then you can go to the Council. Essentially if it's off their land unaccompanied then the dog is deemed to be not under proper control, which is a criminal offence. The Dog Control officer will visit and tell them the rules in the first instance. If it keeps happening the dogs could eventually be removed and put down.