Unfortunately the NHS pre-employment checks can take a while, and inefficiency, unnecessary bureaucracy and poor communication can be par for the course at the best of times and the current situation won't be helping.
YY Sharkyfan, bland/generic references are now absolutely par for the course, organisations (wrongly IMO) are so afraid of being sued for defamation that the vast majority have made it policy to only provide these for some years now - unfortunately some NHS managers aren't always up to date on current trends in recruitment (some of them are absolute dinosaurs who haven't changed their management practice for 20 years or more), and if they haven't had to take references for a few years it can take them by surprise. Many managers still think that the only reasons a generic/template reference would be provided is where there's a problem with the person, which was the case maybe 10 years ago but not at all so now.
You'd have thought it wouldn't be too hard for a recruitment person with their head screwed on to explain things in simple terms to a recruitment manager who is struggling, but not all recruitment people seem able to do so! To be fair a recruitment officer job is usually the very first entry level rung of the HR ladder in the NHS/public sector anyway, often they aren't CIPD qualified or very experienced themselves, and their training and the hierarchical approach of the NHS tends to guide them towards a bit of a 'computer says no' rigid approach rather than applying discretion to a situation.
I expect the conversation went something like
Recruitment person (RP): Here are the references, are you happy with them?
Hiring manager (HM): But these are really generic and don't tell me anything?
RP: These are the references we were sent. You need to make a decision.
HM: I can't make a decision without more information. What should I do?
RP:These are the references we have, the process is that you should make a decision....
HM: ....
RP: ....
Hence when you are emailling, the RP says the hiring manager needs to make a decision, but the HM says they are waiting for recruitment to tell them what to do.... What needs to happen here is that (probably a more senior) HR person or manager needs to intervene to either say that it's now standard to OK bland/generic references and it doesn't mean there is any cause for concern OR that if the HM has genuine questions/information they need (other than general reassurance you are OK/a nice person etc), work out how they can go about getting that, e.g. through a personal conversation with your referees (although understandably your referees may not be willing to do this if their organisation's policy is not to do so) or asking you to provide more evidence or similar.
You could see if you can ask the next time you speak to recruitment to speak to the recruitment manager or Head of Recruitment (who probably won't want to be bothered but may help unblock and refer you to the right person) or you could do as TheHighestSardine says and try and reignite a conversation over email by copying them both in.... maybe state in that email that it is the policy of your organisation to only provide the template reference and asking what more you can do to provide the information required?