Undoing the hook fastener on the reins and cheek pieces of English bridles can be difficult. Get a purchase on the leather just forward of the little hook and pull it upwards so the end of the strap is pulled free of the keeper. You can now grasp this end and pull forward, taking advantage of the little slot cut above the hole to pull the rest of the strap free of the hook. Free the end of the strap from the second keeper.
If the leather is particularly stiff or thick I sometimes ask someone with stronger fingers for help, or I carefully (so as not to damage the leather) insert a small screwdriver underneath the leather just forward of the hook and pry upwards carefully. The little keepers are very thin and the stitching can rip easily, so be careful if you resort to drastic measures.