PAYE is called PAYE in the UK too.
When I was a KA feighter F/O based in the UK and living in the UK, I paid HK tax. My UK tax bill (paid retrospectively then) had the HK tax paid in that year deducted. I didn't have to front up UK tax or pay double tax.
The difference from Oct is that the company will have to deduct PAYE and pay it direct to the UK Inland Revenue. Whether this will have the HK element deducted is the question being asked now.