Book keeping is pretty much generic wherever you go I would think, it's just keeping the financial records of a company. To be recognised as an accountant though requires you to pass an examination to get certified in that particular country unless they recognise another countries certifications. And in some countries you have to resit the exam periodically.
Book keeping (as far as I know) really just means financial data entry, which anyone can do and doesn't require qualifications. Accounting goes a lot further into the realm of adjusting data and more.
So while I do the book keeping for my work, the accounting is done by an accountant, although there is a fair bit of overlap since we're both using the same software.
In answer to the question, your mother should be fine to go and work as a book keeper in the UK.