"Unable to access Derby Emergency Dental"

I broke a tooth on Friday evening. Phoned my dentist and got the emergency dental number, Called and was asked what the problem was. When I told them it happened half an hour ago, I was told I wouldn't be seen unless I had been in severe pain for days. Why would I wait until Friday evening to call an emergency dentist when if I had been in pain for days my dentist had been open! Called again on Saturday morning, several times, but the automated system would not even put me in the queue. I think this service is inadequate to deal with actual emergencies and is only set up to catch people who don't have a regular dentist.