IVF under the NHS is now part of the 18 weeks rule. This means that you should wait no longer than 18 weeks from referral from consultant to starting treatment at fertility clinic. Now the rule is that 95% of referrals should fall under 18 weeks, so obviously, this means that up to 5% might fall outside and wait longer.
Referral from GP to consultant at hospital should be no longer than 6 weeks, but I believe there are a lot of pressure on gynaecology, so that doesn't always happen. You are entitled under Choice to go wherever you want in the UK to see a gynaecology consultant and your GP should be able to tell you waits at different Trusts (you can also find out by calling the national line once you've been referred or NHS.uk tells you too I think or maybe MrFoster website). Referral for IVF falls under tertiary care (specialist) so choice doesn't apply. Rules in terms of criteria and location of treatment will be specific to each PCT (or more often SHAs) and the consultant, wherever located will have to refer back to the commissioned services by your PCT unless exceptional circumstances.
Hope this helps.