My 2x great grandmother was a Crockford - Mary Ann born 1843 in White Waltham, Berkshire. Bear with me as it gets complicated...
Her father James was baptised 1804 in nearby Binfield, Berks, so his father Benjamin Crockford baptised 1773 in Easthampstead, Berks would be of your Philip and Lydia's generation.
Benjamin was illegitimate but his mother Elizabeth Crockford was baptised in Waltham St Lawrence and the generations before her came from WSL and, before that, from Hurst, Berks. All these places are very close to each other.
I think your Philip is the one baptised in WSL 23 Aug 1789 to Philip and Martha. Philip snr (1752 WSL) was the brother of my Elizabeth. He married Martha Sheppard in 1781 in WSL.
Not sure what type of cousins that makes us but there's definitely some connection although distant enough for me not to have gone that far into it. I had Philip's marriage on my tree but hadn't identified any of his children. I found Philip jnr on Family Search.
I'm still looking for Lydia. I suspect she's probably the daughter of another sibling but not coming up on Family Search.
Incidentally, I've never really looked into DNA testing and had no idea it could give you such direct connections.
Jill