Standard issue L tourist visas for British citizens applying in the UK are now good for 2 years, multiple entries, 90 days per stay. The visa goes live immediately, so the old requirement that you use the visa within 90 days, is now gone. You will need to apply through an agent and pay their service fees on top of the regular visa fee; tourist visa applicants can no longer directly approach the Embassy in London nor the other Consulates in the UK.. The official one for the UK is here:
https://www.visaforchina.org/ but I understand there are some other agents that can also access the Embassy/Consulates. Most people apply to the closest office to their home, but AFAIK there is no restriction requiring you to do so. From anecdotal evidence, Manchester seems to have been the most persnickety about documentation and the only one that wants to do fingerprints...at least that's how it was awhile back. Go the website I linked to, and your questions about fees and what to provide in your application package, will be answered.
5-10 year tourist visas are not available to UK citizens, unless the British and Chinese governments agree on a new visa treaty at some point in the future.