What is the name of the Middle Class equivalent of Estuary English?

Estuary English is established across the South of England from Corwall
to Norfolk, up as far as somewhere just south of Warwick where Midland
takes over.

But there is another standard that you will hear universally over that
same catchment. It derives from the the "cut glass" language of Dylan
Thomas. You can follow both dialects 6.00 am - 12.00 noon UK time on
this London Radio Station where the presenters invariably use
[whateverUcallit] and the callers are likeable taxi-drivers from
deepest Est'ry.

http://tinyurl.com/dubok

[It isn't "Received English" BTW. That is a distinct dialect heard all
over Britain: the Queen speaks it, it is common in Belgravia,
Knightsbridge, on country estates, at Lords, Henley, in Pall Mall and
at the House of Lords].

.