16th century Cunningham family

[wildwitch]

Hi
I wonder if anybody can help me locate my ancestors. My ancestor William Cunningham appeared in England in 1606 and I am assuming he probably came from Scotland. I have not been able to locate him or any of his family members anywhere in England though either. He had a wife named Anne and I am estimating their marriage between 1590-1600. They also had the following children before they arrived in England in 1606: Edward, James, Catherine and probably also Hugh. William also appears to have had 2 siblings: Leonard and Joan/Joanne. I have found a possible match for a baptism for Hew Cunningham son of William in 1597 in Edinburgh, but have no idea if this is my ancestor. William was a labourer. There is a record, which appeared 200 years later (1780s) which suggests the family may have come from Lauderdale, but how acurate this is is unclear.
thank you for any help