smellyharry, you are mistaken,,,there are only a few paths at the end.
Once you have entered all the across entries, you will be left with a grid having 30 empty cells and at a specific position, A little study will show you that from that position, there are exactly 4 paths (two of which are nonsense) from it to the circle in which you arrive at the circle for the 4th letter. Similarly for the circle there are just a few possibilities where to go next. With TEA or a list of towns you can then get the first one fairly easily. Then you will have 17 spaces left and the choices are similarly constrained.