T-glottalization

In English phonology, t-glottalization or t-glottalling is a sound change in certain English dialects and accents, particularly in the United Kingdom, that causes the phoneme /t/ to be pronounced as the glottal stop [ʔ] ^ⓘ in certain positions. It is never universal, especially in careful speech, and it most often alternates with other allophones of /t/ such as [t]^ⓘ, [tʰ], [tⁿ] (before a nasal), [tˡ] (before a lateral), or [ɾ].

As a sound change, it is a subtype of debuccalization. The pronunciation that it results in is called glottalization. Apparently, glottal reinforcement, which is quite common in English, is a stage preceding full replacement of the stop, and indeed, reinforcement and replacement can be in free variation.