Personally I think this looks very much like the Cap Badge for the 'East Yorkshire Regiment' as their badge has a star and scroll on the bottom.
Also upon searching the National Archives I found a Medal Index Card for a Richardson, George R of the East Yorkshire Regiment, Reg No: 11390
Also as you are correct about the Hospital Blues uniform which makes suspect that this is the correct regiment as I see that George is on the Silver War Badge list.!!
11390 Pte Richards. George Richard,
Unit Discharge: East Yorks Reg,
No of Badge and Certificate: 500830
Date of enlistment 1.9.14 Discharge: 17.08.17
Cause of Discharge: Kings Regs 392 (XVIa) Surplus to military requirements (having suffered impairment since entry into the service)
I hope this information help and I hope im correct