Shannigans did not reply.

I thought that you could not have joint nationality with Mainland Chinese.

But HK SAR/UK is possible.

As far as am aware, the only advantage of a Chinese citizenship is the Hukou, and this makes local schooling easier. Other than that, I can see only barriers.

Regards the certificate that you have no kids back home. As far as I am aware, there is no agency in the UK capable of (or mandated) providing such a document.
Probably the usual case of the admin person not knowing what they are doing. Try saying to the family planning that the UK Embassy needs them to provide a letter, making the request and it must cite the relevant regulations.

If you go to Shanghai you may find it easier.

It might be blindingly obvious to some, perhaps seasoned travellers. To those who have never travelled overseas before the procedures can be daunting.

Chinesepod.com
Owned by Praxxis I think. A lot of stuff is free, but the pay for packages offer a lot more. Not too expensive if I remember.

Here are some suggestions for self study, but you will need to become your own teacher. Some of this you will know, and so forgive me if I am trying to teach my granny how to suck eggs.

For a quick start, don't even try to write. Remember that there are many people around the world who can function in business who are illiterate.
Social Chinese will help you a lot, and business Chinese is for advanced learners.

Most books will start you reading using Pin-yin (Romanized notation) but move you up to reading Hanzi (Simplified Chinese Characters) before you get through beginner level. This I found to be a major barrier. The same is true for many online courses.

You can learn to read, without having to learn to write. You can be semi-literate.

I can recommend Pimsleur Mandarin I-III audio. It is expensive, but lots of very naughty people download it free from the internet. This is very naughty and should never be done (snigger). Pimsleur has a good mix of social and professional Mandarin. Level III will take you to intermediate level, without the need to learn to read Chinese characters.

Getting a Chinese teacher also helps with the audio courses, as they can help you practice your pronunciation. Pronunciation is critical in Mandarin, change the way you say a word and change its meaning. For example, to the untrained ear the words for 'buy' and 'sell' sound identical.
Another advantage of a teacher is that they know the vocabulary that you will know, for your level. For example a beginer will have a vocab of about 600 words at the end of the course. Most people you meet will use a full vocabulary, this is frustrating and demotivating.

Find yourself a friend, not a language partner. Ideally someone who speaks almost no English, but likes the idea of a western pal. Make sure it is someone you have something in common with. I talk my wife's driver about cars and sport. If you get a language partner you may spend most of the time speaking English.

You can go with a Chinese speaking person to the market to buy stuff. There is more than this to haggling. Once people know you are not a spy and want to practice Chinese you can speak about buying, selling, trading, transport, lead times, import and export (in the fruit market), supply chains; its not all about prices and haggling. It might also help to become boozing buddies of local traders (trading company).

BUT you will need to pre-learn essential vocab first. You will need to be your own teacher.

In short. My recomendation. Pimsleur audio, with occasional input from a teacher to correct pronunciation, don't try to read, and find a buddy who speaks poor English. Then find a buddy who speaks better English to trawl the markets and befriend some local businessmen.