I go regularly (at different times of the day). I have never not been able to find a parking space. Granted sometimes I have to part right at the furthest part of the “overflow” car park, but I always manage to park somewhere. At the end of the day the Hospital is getting bigger and busier and it attracts a lot of traffic. The car park has expanded over the years to reflect this.
It is worth noting that some hospitals charge people for parking.