That's terrible. Poor you, poor garden and, sorry but, poor dog too. It is the owner who is at fault!
CONTROL OF DOGS ACT, 1986 states
9.—(1) The owner or any other person in charge of a dog shall not permit the dog to be in any place other than—
( a ) the premises of the owner, or
( b ) the premises of such other person in charge of the dog, or
( c ) the premises of any other person, with the consent of that person,
unless such owner or such other person in charge of the dog accompanies it and keeps it under effectual control
The dog obviously was, and from the sound of it is, not under effectual control.
Is the neighbour approachable? She should at least offer to pay your replacement costs.
You might start WW III but... Contact the local dog warden to see if she have a dog licence. Contact the law enforcers about breaches of the Control of Dogs Act and contact a solicitor about sueing for damage...
Maybe you will settle for doing the work yourself but notifying the neighbour that you won't hesitate to go the whole hog if she doesn't act like a responsible dog owner in the future...