Don't know about cheap but I got a small dog flap from P@H for about £30. I think you can get them cheaper from Argos - it's the standard rectangular one but twice the size of the cat one. As it's got a long magnet it stays shut a lot better than any of the rounded ones that just have ickle tiny magnets. All three cats use it - I wont say happily because Sammy hates it and refuses to use it unless there's no-one home (to see him?). The P@H one comes with a free rubber flap, and to lock it you basically slide a bit f plastic across it, so it's not a 4-way one or anything.
I used to have a 4-way one, but I locked the cats in once s I could catch Sammy and take him to the vets, and forgot to unlokc it before we went. Seth decided he was going out anyway..I assume he just went through it at full pelt, the lock was in bits when I got home and he was outside...