You are assuming Percy's half brother was from his mother's side - just because his father wasn't listed on his birth certificate doesn't mean they didn't know who he was (of course that could well mean you are never going to find them)
I am almost certain they had the same mother. Percy had contact with them and (John?) visited her in the asylum also.
Mum said they were full brothers and their name was Platt also but that I am not certain of.
I am hoping Percys Military records reveal something and I will order the marriage cert for John and Doris Platt .. apart from that I am still struggling.
The only thing I have for certain is her name and the fact she died around 1950 in an asylum.