[Does this refer only to England, or perhaps only to Britain? If so, it should say so. Is the use of capital letters, rather than "permit to travel" essntial? If not, then the article should be moved.]
A Permit to Travel is a halfway stop to buying a train ticket. You can buy one to any value, and the permit will show how much you paid and where it was bought. This can be used as part or full payment for your real ticket on the train.
This means if a guard doesn't reach somebody until a few stops after they got on, then they are unable to claim they are only making the shorter journey. If somebody is completely missed by the guards, then it ensures at least some money is collected.
Penalty Fare inspectors may enforce the system, fining people who did not buy a ticket or permit before boarding the train.
Permit To Travel can be found on some Arriva services.