British schools teach, or should teach, Standard English. Standard English is the language used in most published writing and spoken in contexts such as education, broadcasting, the law and public administration. The most authoritative source on English vocabulary is, as others have said, the OED (Oxford English Dictionary), not least because it illustrates its definitions with citations showing the way in which words have been used in the past and how they are used now. It is, however, a commercial publication and has no standing in law or with any other kind of authority such as an academy.
The grammar of Standard English is codified in academic works such as the ‘Longman Grammar of Spoken and Written English’ and ‘The Cambridge Grammar of the English Language’. Like the OED, they have no official status, and it is doubtful whether most English teachers consult them or even know of their existence. In spite of this, and apart from a number of disputed areas, there is widespread agreement on what constitutes Standard English, or at least on what doesn’t constitute it. This is partly because the differences between Standard English and other dialects are actually quite few in number and partly because examples of Standard English are freely available in newspapers and on television and radio.
None of this, however, means that all children leaving British schools speak and write Standard English. They may continue using their own dialects and there is no reason why they should not do so in the appropriate context, but if they have not been effectively taught to communicate in Standard English their life chances are diminished. Unfortunately, many people, including, no doubt, some teachers, confuse informal English and social and regional varieties of English with incorrect English.
That’s a long way of saying that there is no formal basis on which Standard English can be assessed in the UK. In assessing children’s competence in it teachers and examiners must ultimately rely on their own judgement and experience, consulting academic sources as necessary.