Welcome panda, but sorry to hear you've had such a difficult time. Unfortunately I know very little about your condition, but I can talk a little about coventry. They test specifically for uterine natural killer cells (uNK) rather than blood NK. There are other places that test for blood NK and they can give different results. If you go to coventry and it comes back normal it might be worth looking into this too.
If your uNK level is greater than 5% coventry recommend prednisolone, normally at 20mg per day, from bfp to 13 weeks. They may also prescribe heparin and progesterone. Your circumstance is a bit different to most of the women here in that you haven't had a series of recent miscarriages, but coventry will test after only one mc, I believe, so your loss 5 years ago should be enough for them to agree to test. I gather that if your level is extremely high then they may offer some treatment before bfp to bring it down before conception. I'm not entirely sure what treatment this is, but they'd discuss this with you at the consult.
I take it you're not on any treatment for your arthritis currently (like methotrexate?)
I'm really not sure about whether you will need extra help to fall pregnant. Most of the people who visit coventry that have been on this board have had either normal or moderately high levels. I don't know anyone whose level was so high that they got help before bfp, so I presume this could help if that's your situation. It also depends on whether it is this or something else that is causing the fertility problem of course. I think the fact that you have been pregnant naturally before (albeit when you were on treatment) is a good sign, as perhaps it suggests you just need the right treatment again, but I'm sure that's not much comfort at the moment for you, so I hope that doesn't come across as that infuriating 'at least you know you can get pregnant' line that people who have no idea reel off.
It would be worth contacting coventry I think to ask their advice on whether it would be worth going. The admin person is called kerri geraghty if you want more info. If you do decide to go, you contact them when you ovulate (testing with the sticks), and they will book you in 7 to 10 days later. There is normally just a single appointment then everything else like results and follow up are done by email and phone. It's £360 one off fee. They normal only have appointments Mondays and Fridays. Hope this helps. If you have any more questions then feel free to ask anything. Good luck x