Why I always hear British pronounce T's as glottal stops? I have been told only cockneys do that but it seems everyone else, I hear them in TV, Onlines, Radios everyone I don't know if it's true or it's only my ear.
The glottal stop was and is a characteristic of Cockney English, but its use is spreading. People talk of Estuary English, which is spoken quite widely in London and around, which has some of the features of Cockney English, like the glottal stop. You will hear people using it, though there are plenty who don't like this. Features that were confined to specific regions are sometimes appearing in other regions nowadays, and thisis one you will find used by many speakers.
Tony Blair spoke RP when abroad or on formal occasions, but when speaking to a domestic audience would sometimes use the glottal stop. The younger princes use it, though combined with the traditional long vowels of RP, so their pronunciation is a bit of a weird hybrid to my ears.