Ok, so I'll provide my own answer. Lydia Middleton does not seem to be related to Kate Middleton, but Samuel Purdue is. Having Alexander Cox as an ancestor, Samuel has a link with some British nobility including the Talbots. Kate Middleton also has some Talbot ancestry through Sherrington Talbot if her lineage as detailed in "the Times" is accurate. Incidently Samuel Purdue is also related to William through the Despencer line and the St Johns.