Hi, Annette -
Thanks for your response!
No, there isn't a burial for Ellery 1737 on the NBI. But sadly there is one in the Exning records - poor little lad didn't last long: buried 15 Dec 1737.
Ellery 1739 lived to a ripe old age and was buried in Exning on 6 Mar 1821 aged 82
So did Brand. He was buried 26 June 1821, allegedly also 82.
I know a number of researchers have decided that Brand must be a son of Ellery Snr and Elizabeth Collins, because they were the only Parrs in Exning at the time who were baptising children. But those same researchers say Ellery Snr was born in 1703 in Exning, and HIS father Ellery was born in Chatteris in about 1680. Whereas they were actually born in in 1666 in Burwell and 1706 in Isleham respectively! Some of them have even invented a completely spurious Ellery because they have failed to realise that Ellery 1706 married three times and had 18 children. He was STILL fathering children the year he died in 1774. A very lusty man, which makes an illegitimate son with local village maiden Elizabeth Brand seem quite believable!
Unfortunately, just a mile or so up the road was Burwell, where they had Parrs coming out of their ears - so there's no telling which Per/Parr/Purr young Elizabeth was misbehaving with!
The baptism date of 1744 for Brand Per Brand doesn't fit with the alleged age at death, but who is to say that is correct? He had outlived his wife and she was probably the only one who knew....
It's a mystery. Certainly, he was using the name Parr by the time he married, and one of his grandsons was Joseph Ellery Parr, so there is almost certainly a relationship which may well have been acknowledged as he grew up - but no evidence.

I am hoping to turn up a will or some other evidence of that kind which might identify his father. And was half hoping that someone might already have done it!
But never mind, back to the drawing board.