Word for someone who adopts lower class mannerisms

In the UK this is often called 'Mockney' from mock+Cockney.

Cockney
Linguistically, Cockney English refers to the accent or dialect of English traditionally spoken by working-class Londoners. In recent years, many aspects of Cockney English have become part of general South East English speech, producing a variant known as Estuary English.

Several British politicians are guilty of this, in feeble attempts to make themselves more appealing to the working classes.Here is Conservative MP George Osborne at it, as recorded by The Telegraph newspaper.

Ex-Prime Minister Tony Blair was also guilty of it.

An equivalent expression in AmE would be to say that someone has "Gone/went Ghetto"/redneck/cholo/trailer-park.

Certainly with regard to the accent (but with associated aspects too)- mockney:

"pronunciation of English by someone who pretends to speak like a cockney, in order to seem as if they are from a lower social class".

The result of the popularity of such style, though, is inevitably to raise the staus of the formerly "lower class", until the gesture becomes meaningless.

Such a person might be referred to as a poser or wannabe: someone who acts or dresses in ways they believe align them with a different (e.g. poorer or "lower-class") culture, thereby posing as relatable to people in that culture or even as a member of that culture.

These terms don't suggest mockery of the target culture. In fact, they describe someone who admires a culture enough to emulate it. The terms are used derisively, as such people are generally perceived as foolish.