Hi
You will need to have been a resident AND a tax payer in the UK for a minimum of 6 months to qualify for NHS treatment - any NHS treatment. To qualify thru your partners national insurance (tax) contributions, he needs to be your husband.
As you're already 22 weeks, you will not qualify for NHS treatment in time for the birth.
It may sound disappointing but many of us here can assure you that an NHS birth isn't particularly fabulous....
Its unlikely that you will find an insurance company which will cover you for any pregnancy/birth treatment as you are already pregnant.
The only option for you and your husband is to request that his new employers pay for all of your maternity/birth care as part of your relocation package. If I was in your situation, I would not set foot outside my country unless I had this in writing.
You can pay for private maternity here (I am currently considering this despite being entitled to NHS treatment as my last birth wasn't great). It will cost you between £10,000 and £13,000 (for either a VB or C section) and this is assuming they are straightforward and you go home within 36hrs.
As for care for your baby - your baby will be born in the UK and therefore entitled to NHS treatment as soon as he/she is born. This means that if you give birth privately and pay for it and your baby needs NICU or special care, he/she can be tranferred to NHS and treated for free. And NHS neonatal/children care is fantastic!
My DH was offered a job in Singapore when I was last pregnant, we had to turn it down as Singapore Immigration would not let me enter Singapore and give birth there, I had to give birth elsewhere and then join/rejoin DH (they don't like to give out Singaporian passports). So job was turned down. Again we would have had to pay for the birth as I would have left the UK and spent 6 months outside UK and lost by free NHS entitlement.
Hope that helps. Relocating can be depressingly complicated at the best of times, I hope it works out relatively stress-free for you.