You can apply for an NHS pension forecast yourself, momoko, HR don't have to do it for you - I used to ask the person in the payroll department who dealt with pensions to apply for one for me. I've done that several times over the years, just make sure what they are forecasting for me when I chose to retire.
Surely if you start paying into the state scheme now, you would get something (even if not very much) when you retire? It's very easy also to apply to the Pensions Agency for a forecast if you are already paying in.
HR may not be the best people to ask, IMO - your Trust's payroll department is a good place to ask, that's who I went to to get pension information.