Can depend on when your Dad died, officially the NHS updated the register till the 1990s, but I have come across some that died prior to that yet were still redacted. In that case you'd need to send a copy of his death cert to release his record. I have done that a couple of times, gave all the details I knew, name, d.o.b., copy of death cert and, from memory, it didn't take too long to release the record.
If you have a sub with FindMyPast (or know someone who does and will send the request) they do it free. whereas I believe the NA charge a fee.
Boo