"Our" Elliots are reputedly from Yorkshire , and one of the family tales is as follows :

The Elliots were farmers around Marston Moor where one of the principal battles of the English Civil War was fought . One of the Elliot girls was by a farm gate when a group of horsemen appeared , the leader of whom tuned out to have been Oliver Cromwell . As she opened the gate for them she was asked " whom do you support " . Showing wisdom beyond her years as she could not distinguish whether they were Royalists or Roundheads she answered " you my Lord ".

I have not yet found any references to the Yorkshire Elliots but here are some general notes on the Elliot Clan . 
The Elliots are probably of mixed Viking-Saxon-Celtic origin as are many of the Border families . Early records show them as fighters and horse and cattle thieves . All the border clans formed tenuous relationships with each other, (Armstrongs, Croziers, Nixons and Buccleughs). They fought for and against the English as well as each other.