We can google all sorts of manufacturors' names with "child's car" and I forsee a lot of wasted time analysing the results - particularly for those companies with a fairly common word as their brand name, such as Morris or Star, but just think how many results you'd get from Standard!!! Even before t'internet we had difficulty finding "Standard" references in our bound volumes of Autocar/Motor/Automoter Journal.
......and we have a winner!
These photgraphs come from an article on the Standard Motor Club website, written by Malcolm Buckler, son of a well-known name on here, Derek Buckler himself. According to Malcolm, the car had been in his family for a good number of years, and was believed to be the product of Standard, probably built for a son of Sir John Black. His father had taken the car in lieu of a debt. The only detail which references Standard is the badge on the radiator shell which quite frankly could have been applied by anyone who'd happened to find a spare badge. It is of course possible that Sir John Black asked some apprentices to modify a Rytecraft for his son - the rear bodywork is unlike most Rytecrafts and could have been bespoke.
My personal belief, unfounded of course, is that this is one of those family stories that has become confused over time, rather like antiques that have been in a family for years and purport to be something valuable. I reckon there never was a Standard connection.
Thanks for solving this one, Allan. I thought it might be a BH candidate.