It’s curious that there is a Rhoda Smith on both sides of this story - his adoptive mum was born Smith 1870 At Daglingworth glos and his true father Edwin’s mum was Rhoda Budgett b 1834 nunney somerset, married Benjamin Smith of Walcott, bath.
So apart from the Smiths all coming from the West Country into Lambeth, as well as George teagle, I don’t see any blood or marriage connection for the Smiths.
Jane Simpson’s folks are x Ireland, per 1871 census at woolwich.
Giving a child to another childless couple happened in my husband’s family - his ggm to her aunt, and she was a replacement for her elder brother who got to come back into the family when he was old enough to work. Sad life for ggm who had a wealthier home to grow up in but was never able to get past feeling abandoned by her own mum.
Salute,
Janelle