my friend was getting puncturues on a weekly basis (thorns, glass, stones); I fitted schwalbe marathon plus as well as slime filled inner tubes and she has not had a single puncture so far (and I should know as I am the mug who would fix them )
Narrow mud tyres with very pronounced widely spaced blocks. Very narrow ones, like 1.7's, they cut through the slippery slimey stuff and don't clag up, nor do they jam in the stays.
I've got some old Spesh Extreme Master/Extreme Control kevlar beaded ones, that are reserved for wet days on the South Downs and in Wealden clay. Bought three pairs when they stopped making them. imo round here (so long as I stay away from the sandstone bits of the Surrey Hills) I've yet to find a better winter tyre for chalk/clay for my style of riding. But I admit they look odd on my Boardman Pro HT, just way too skinny for a modern bike.