I phoned the dentist I go to, explained that I was applying for dentistry and wanted to gain a bit of work experience and could I come in and observe. They were very helpful and the practice manager sorted it all out. Took a few days (maybe even a few weeks if I remember right!) to organise with the dentist but easy enough. I wasn't able to observe the hygienist (her choice) but she was happy for me to go in and ask her lots of questions.
From there I was given a contact at the hospital so I organised to go along and observe there, they had a programme in place already so that was very easy to do.
You could try orthodontists, dental labs, etc too. It's all good experience and shows you are keen (to the dentists too that you want to go along too), I was told that our dentist don't always do work experience as they got rather a lot of bored and uninterested people sitting in a corner! So only took on people who seemed very keen. Perseverence then!!!
You won't have a dentist there (editing as I didn't read properly...) I'm guessing but going along personally to a few might make a good impression?