You having a Hong Kong Permanent Identity Card means that you are (or were) a Hong Kong permanent resident. Neither having this card nor being a Hong Kong permanent resident means that you are a Chinese citizen. Hong Kong permanent residents can be Chinese citizens or foreign citizens. If you had an HKSAR passport, that would tell us that (at least Hong Kong thinks that) you are a Chinese citizen, as HKSAR passports can only be issued to Chinese citizens with Hong Kong permanent residency, but you don't have one so that doesn't tell us anything.
We can try to infer some information from your being a Hong Kong permanent resident. According to the Hong Kong Basic Law, only the following 6 categories of people are Hong Kong permanent residents:
- Chinese citizens born in Hong Kong;
- Chinese citizens who have resided in Hong Kong for 7 years;
- Chinese citizens born outside Hong Kong to parents in (1) or (2);
- non-Chinese citizens who have resided in Hong Kong for 7 years;
- children under 21 born in Hong Kong to parents in (4); and
- anyone else who prior to the handover had right of abode in Hong Kong only.
You were not born in Hong Kong, nor have lived in Hong Kong for a long continuous period of time, so the only basis that would probably apply to you is (3), which would mean that the Hong Kong government must have determined you to be a Chinese citizen.
Determining whether you have Chinese nationality is complicated in your case because Hong Kong is involved, and the application of the PRC Nationality Law to Hong Kong and Macau involve a bunch of special rules that are not consistent with the original law itself, so is very hard to try to reason about.
Usually, Chinese nationality for a child born outside China is determined by Article 5 of the PRC Nationality Law, which says that a child born abroad to at least one Chinese citizen parent is a Chinese citizen, unless at least one parent was a Chinese citizen who has "settled abroad", and the child has foreign nationality at birth, in which case the child would not be a Chinese citizen. You had foreign nationality at birth, so it hinges on whether there was at least one parent who was a Chinese citizen who had "settled abroad" (interpreted as having foreign permanent residency or right of abode) at the time of your birth. Your mother was a Chinese citizen; did she have British (or any other country's) permanent residency at the time of your birth? Your dad was presumably not a Chinese citizen at the time of your birth, so his right of abode shouldn't matter.
One of the special rules for Hong Kong says that all Hong Kong residents of Chinese descent born in China including Hong Kong are Chinese citizens (I'm not sure what the basis of this from the PRC Nationality Law is). If your father is of Chinese descent, and assuming he was born in Hong Kong, that would mean he is a Chinese citizen. But you were born outside Hong Kong before the handover, and it is unclear whether your father would be retroactively considered a Chinese citizen for the purposes of determining whether you would be a Chinese citizen at birth, and if so, whether his foreign citizenship would be considered a foreign right of abode which would cause you not to have Chinese citizenship. (Another of the special rules regarding Hong Kong is that Chinese citizens of Hong Kong can voluntarily acquire foreign nationality without losing Chinese nationality, even though they should lose it according to Article 9 of the PRC Nationality Law. Given that the rules are permissive regarding Chinese citizens of Hong Kong holding foreign nationality, it would seem odd if that foreign nationality prevents those parents from passing on Chinese nationality to children born abroad, so I don't know if there are further special rules regarding that.)
In any case, when in doubt when filling out applications that ask for all of your nationalities, you can always be honest and say you're not sure about whether you also have Chinese nationality, because it's not uncommon for people to be not sure about a nationality they have never exercised. This way, you wouldn't have potentially given incorrect information, and they probably won't care about whether you have potential extra nationalities for the document you are applying for anyway.