If you want to know for a fact, consult a solicitor but this is where you stand according to several countryside law books (my interpretation) :
First, you must be clear between the different trespassing offenses.
1) simply crossing on to another's land is a civil offense, in other words the landowner would have to prosecute you.
2) Crossing on to another's land with a gun, is armed trespass and is a criminal offence, in other words the police would prosecute you.
3) If a dog is pursuit of game on land where you have permission, and the dog continues it's pursuit on to land where you