"Wait very long time to have a first appointment..."

Since my wisdom tooth is very difficult to remove, I was referred to Royal London Hospital by my local NHS dentist. I faxed the referring letter dated 18 March and have just received a letter from Royal London Hospital today (10 April) for a first appointment on 13 June. It is nearly 3 months for this referral. But the first appointment doesn't mean to have any treatment so I may need to wait longer to have a treatment. The pain from the wisdom tooth is very annoying, that pain makes me dizzy as well. It seriously affects my daily life. I take the painkiller nearly every day. I did ring their Central Appointments Office but they said they cannot provide an earlier appointment for me unless there is someone cancel their appointment so I have to call every day to check. It is too long for the waiting time and I would like to know is there any other way to speed up the appointment date. It is ridiculous to take painkiller every day anyway :(