I think it really depends on your hospital.
The dr referral to IVF took a few months (referred in November, saw them in about Feb or so?)
But once I got approved I was able to start IVF on my next cycle, although because the # days in the cycle was getting erratic they delayed it by 1 to give me the pill for 1 cycle to regulate it.
(The consultant(?) who approved me for IVF said that they'd worked very hard to get the queue down to basically nothing.)