I'm a little surprised at the notion that British English is more likely to preserve full pronunciation of 'T's.
In my experience, and in my own speech, it is quite common for British accents to completely replace a T with a glottal stop, unless one is being very deliberate with their speech, especially amongst younger speakers.
In my experience, and in my own speech, it is quite common for British accents to completely replace a T with a glottal stop, unless one is being very deliberate with their speech, especially amongst younger speakers.