my work involves digging the foundations by hand, most of the time. i would not dream of getting a machine into the back of someones garden, destroying their lawn, shrubs etc.the builder should have seen what was in front of him the first day he came to look at the job to give you a price. if the neighbour does not want them to go through their property then by hand is the only way.He should have asked before he worked out his price. if you have already agreed a price, do not change it to accomodate his error, if you start doing that he will keep saying you have to pay extra etc.