the Queen's (or King's) English used to be the term for what was considered to be the English spoken and written by educated people of the upper social classes. The King's English (1906) was the title of a book on English usage which was influential for many years.
BBC English refers mainly to the accent used by BBC news readers from the early days of radio up to, and beyond, the 1960s. It was regarded at the time as a standard to which we should all aspire.
For linguists, RP, received pronuciation, was a 'neutral' term for a 'standard English' that was approximately the same as BBC English.
In more recent times linguists have tried to be non-judgemental about regional and class-associated accents and dialects; the BBC has employed an increasing number of announcers who have a 'non-BBC' accent; RP itself is changing.
So, the expressions about which you are enquired have little real meaning today.
- For Teachers