How do you prevent water penetration of non cavity walls?

How have the walls been insulated and what thickness is the wall?

Check the guttering ent leaking. Check for a roofing leak. Check the pointing of brick work, if rendered check this is solid and no holes Make sure the damp proof course in brick work is present and also damp proof course should not be breached and be 3 courses of brick above ground level. You could use a water repellent brick seal on the out side of the wall.

Check there are no leaks in the roof space mainly on the side apex check the apex mortar as water seepage can seep through the cavity also check the exterior walls if rendered check for any holes or cracks if brick check condition of mortar also check damp course if any as rising damp could be an issue treat pourous walls with a penertrating damp water repellant sollution or give a good coat of paint if the exterior brick work is fine and the roof pourous walls would be the problem so treating walls with a good paint or weatherproof it