Hi there, we've been through a lot of testing over our period of trying for 2 years and are now about to start IVF due to unexplained infertility, so listing below in case you might find it useful / see if can get on NHS / decide if you want to consider private testing.
Bloodwork - STI checks, thyroid function and AMH main ones
Pelvic ultrasound - check lining and ovaries - how many follicles you have
HSG - check if tubes are clear
Sperm analysis and DNA fragmentation for my husband
All our results came back within range, which was frustrating as we didn't have a symptom to blame it on.
We did our bloodwork with Randox and did a full body MOT which was £350, but you get tested 6 months apart - its tests over 100 things, but what I found useful was the thyroid function, vitamin deficiency, prolactin (you don't want this high as it can contribute to infertility), testosterone to name a few and I think its £50 extra to test the AMH (one payment and they will test twice over 6 months).
We did our pelvic ultrasound with ultrasound direct, it was £145 which was much cheaper than doing it at a private hospital, we were seeing costs in the £300 range. My follicle count went from 24 to 10 in a space of 2 years, which is still within range, but it was a bit of a shock to see a drastic drop given I'm under 35.
We did HSG with Lister clinic and it was £500, to get this on NHS you need a GP referral, otherwise have to go private. We were advised no need to get HSG if we were planning on going down the IVF route as the process skips the needs for the tubes. It's meant to increase fertility by about 20% even if they aren't blocked because it flushes out the mucus but its a little uncomfortable.
Sperm analysis and DNA fragmentation also at Lister clinic and London Andrology, it was a little over £2.5k - this was for our final reassurance we had tried every test we knew of to get some kind of diagnosis, but probably wouldn't recommend DNA fragmentation which is really expensive. A private sperm analysis in London is generally under £200.
Hope this might be of some help, and good luck on your journey x