Back in the 1975 when I went to Ireland to get married my wife to be had a friend who carried out family research.
He carried out most of research into family name.
When Dad was alive we started to investigate our family tree and during this time so many conflicting stories were identified. The similarities between Toghill, Tothill, Toogill and other derivatives was a puzzle.

We contacted Burkes Peerage and others to see if there were any records or information.
We commissioned a report, good idea at the time, into the Toghill Family.
One of the links given was the Heritage Research Centre in Dublin.
On one of our visits to see my wife's family we went to the Centre with as much information as we had.
For another fee, another good idea at the time, they identified a link with the o'toughail from Co Donegal.

During the 15 and 1600 there was a great deal of religious based movement due to the changing fortunes of the Catholic and Protestant faith.
The movement of Catholic Scots to Catholic North of Ireland increased tensions for Protestant Irish.
Religion was a focus of so much religious conflict from Puritan Cromwell to William of Orange and many Irish protestant families left and come to Britain.
During the reign of William of Orange, Dutch land reclamation techniques were brought to England and a lot of work was undertaken in the Bridgewater and Bristol area.
This activity was very labour intensive and would have been an attractive employment opportunity,

We thought that with this and the Bridgewater canal being built in the 1700 and the influx of Irish navvies at that time it could be one reason for the large family connection with this area.
It was also common for the English timekeepers to anglicized the foreign workers names.

There was already a local area outside of Bath call Tog Hill and so o'toughail could easily have become Toghill.
The O'toughail clan was part of the O'Toole family.
The coat of arms was identified and authenticated at that time.
True or not has yet to be determined but to date most plausible of all ideas