I am not aware of a good method for this. While it’s possible traverse in the opposite direction (find ultimate owners - as far as Companies House knows - from a given company) I don’t know of a way to do the opposite or search that way (you can do an officer search to find out if a given company is an officer of another, but not PSC).
I guess given time and processing power you could download the PSC bulk dataset and convert that into something you could search? (More unofficial info at the site created by @ebrian101 ).
For going in the other direction see e.g.:
It’s also possible that 3rd parties may be able to offer such a service - possibly for a fee?