I DOUBT IT. I don't know how great tits hurt you but stop spreading lies.
Parus major is an insectivorous bird that has its diet bulk in arachnids, while has a preference for caterpillars when their eggs have hatched. Like other tits, it will forage (sometimes along other species) and they tend to eat mostly seeds (with a predilection for sunflowers).
In extreme circumstances, it has been seen hunting and eating roosting small bats (pipistrellus are varely 3in), and large nuts (hazelnuts) by hold hammering.
There is no reported case where a great tit has hunted down a bird or a rodent.
If you have such evidence, please submit it because you'll cause quite a stir.
Also the "they also hunt birds" is a big ball of FUD, as they tend to spend winters with other species to gain warmth (and even forage together).
Note: Most animals in dire circumstances can behave as an opportunistic carnivore (as explained with pipistrellus).
