A very belated reply but there are two unrelated Ekins/Eakins families. One is an English gentry family from Northamptonshire. The other is an Irish family: Scottish planters, originally from Ayrshire iirc. Their name is an Irish corruption of the Scottish Aikin family name.
Some of the Irish family seems to have come over to Liverpool in the mid Nineteenth Century and again iirc, had a branch in London.
The English Ekins family have also spread to other parts of England.
I hope this helps.
John