"George Osborne and Tony Blair resemble the Kray brothers"

That surprising claim comes to you direct from the Dean of the University of Buckingham school of education, Barnaby Lenon. I've cut it down slightly - you might think he was perhaps referring to their perceived criminality, but no, it's their accents he is talking about. 

It's been a while since I've heard the term Estuary English. It's the kind of English that people speak all over the southeast of England. Jamie Oliver, for instance, speaks the Essex variety. We don't tend to hear it called that so much any more because you really only need a term for an accent when you're singling it out for some reason, for criticism for example, and lately (now that the speakers of Estuary English are the ones making the criticism) people's critical attentions have turned to what the young people are speaking, which is not Estuary English. 

So now who is speaking it, if not those damned teenagers? Well, Tony Blair, George Osborne, and Prince William, it seems. Yep, he who ought to be speaking the Queen's English is "lapsing" into Estuary English, according to Barnaby. 

He seems to be commenting on research by someone else, Graeme Davis, who has been quote-bundled into this article in a way that conflates his findings with Lenon's, which may well not be terribly accurate. Davis says that we are seeing levelling, which is when different accents become more similar to each other and 'posher' accents become less 'posh' to fit in a bit more. This is a well-known and not very news-worthy finding, but it is true at least. As Lenon says: 

It is very important when you are with non-Etonians to try to conceal that you are an Etonian. They do not want to appear to be upper-class because being upper-class these days is not a good thing. If you are in politics, for instance, you want to appear to be a man of the people. 

Sure. Right now, populism is in. It's good to look like you're a man of the people. (You're totally screwed if you're a woman, by the way - no such thing as a woman of the people.) 

But he also says: 

George Osborne and Tony Blair are both prone to lapse into estuary English so they resemble the Kray brothers rather more than the private school background they come from. Remember the Old Etonian Prince William saying: ‘I need to check this with the missus.’

I mean, the Kray twins didn't have terribly pronounced features of Cockney but they did not sound like George Osborne. There's clips of them talking on YouTube. You can go and listen to them. They're just not the same. 

I would say that most Etonians and Harrovians these days go out of their way to employ an estuary accent.

Those poor old Etonians and Harrovians, held back by their posh accents, disguising them to try to fit in and get on in life. 

Really, what's going on here is that Davis has found that prep school boys' accents have continued the trend we've been seeing for many decades of becoming less distinct from a more everyday middle class English, features of which are shared among many varieties (glottal stops for 't', for instance). Essentially, RP is no longer so distinct from the other Englishes spoken in the London area, and has been on this path for many years. Politicians and young royals no longer get so much benefit from the authority conferred by a posh accent, and gain more benefit from being relatable (perhaps - Jacob Rees-Mogg, Boris Johnson et al still play on the private-school vibe). So far so expected. Then this chap in his new job (mis-)interprets this research for a splash and uses a term that was derogatory in the 00s to spark the old 'mockney'-bashers' ire, and makes a daft claim that doesn't stand up to a moment's scrutiny.