Thank you for your posting. I believe base on your information we have a common ancestor in Thomas Allensby our 4th Gt Grandfather from Ely Cambs, making us 5th cousins. My grandmother was an Allensby her father came from Ely.
The Allensby name is not common, and I agree with your mother from a family history point of view it seems to me that all those who descend from this line are related.
Its nice to find another cousin.