Is it still possible for a UK Citizen to obtain a China Visa in one day?

Hi, as I know, you can use express service which your can get it on the third working days. Rush service is not available.

Depends how you are getting there. If you are flying to HongKong and planning to cross the border from there, you will be able to apply for temp visa valid 5 days on the border between HongKong and China. This is the case at least for Huanggang Port border
As far as I'm aware, this service is not available on Futian border.
It should take up to 30min to get temp visa.
It cost roughly around 400 RNB.
After 5 day you will need to return through the border, get another temp visa (if required) and then you can go back for another 5 days ... and so on ...