Hi tutor1, I would suggest contacting the British consulate in HK, they are very helpful and answer questions very quickly.
Were you born in the UK? Do you hold a British passport? If so then your child should automatically get British citizenship regardless of where they are born and regardless of your SO nationality.
The problem comes if you are British by descent, for example, I am British but my parents were working abroad when I was born. Because my husband is not British and our son was born her in HK, he is not entitled to a British passport- very annoying, and rather unfair!
Once your baby is born you just need to apply for a British passport as you would apply for once yourself.
However if your child is not born in the UK, and they go on to marry a non British citizen, and their children are born outside the UK, their children will not be entitled to British citizenship!