Tis a temperamental letter - touchy, testy (tut tut) and tense. Mind you, given what's happening to it in contemporary Britain, the odd temper tantrum is perfectly explicable.
The influence of "Estuary English" on pronunciation is particularly marked in the case of poor old t. In some words it has been silent for a while (castle, listen, and French source words like mortgage and ballet), but that silence encroaches further every day. For a naturally talkative letter (tending indeed to tittle-tattle) this must be terrible.
Pronunciation of the word often, for instance, varies between generations: older people often pronounce the t, the younger generation seldom does. Final t in words like got and nought seems to be disappearing in the same way, and in extreme Estuary pronunciation the glottal stop has already removed the t sound in words like bottle and water.
There's also a problem with the th sound, which linguists will tell you is actually two sounds - voiced th as in this and unvoiced th as in thumb. Most teachers, however, have little time for such niceties, engaged as they are in the daily struggle to convince children that th exists at all. A generation brought up listening to television personality Jonathan Ross (and, unfortunately, the majority of children's programmes on the BBC) generally finks vere's no such fing. One way to convince them is to emphasise articulation: you put your tongue out for th, while fv involves connecting the front teeth with the lower lip. Articulation is also the best weapon against the glottal stop et al. You don't need to institute elocution lessons - just inform the class that to learn certain spelling words "We are all going to talk posh". Then assume a Lord Snooty accent and invite them to join in.
With any luck, this will help with your class's spelling, but the pronunciation is almost certainly a lost cause. In many words t will soon be as silent as the k of know and the w of write - and for exactly the same reasons. Only the spelling will linger on to remind us of the way our forefathers spoke. Isn't language wonderful?