Try cleaning the gulley out, (dont go sticking your hand in there though without a stout pair of rubber gloves on as a minimum!), and see if the water runs away! Drain looks blocked and so the water is backing up and finding it's way inside. Once you've got a clear drain, look for where it's getting indoors and plug the gap.
Your pics are out of focus, so more pics from better perspectives will help. Perhaps if you stood back a little.
The first pic shows the rising main and a capped copper stub coming out of a concrete floor - a definite clear pic of wall and floor is needed please. Presumably the wall is damp? Have you examined the whole back wall at a low level?
The gulley appears to have had recent repair work with a rim of mortar?
The concrete path surface seems to have raised the finished surface level - perhaps bridging the DPC and causing fitting difficulties for the gulley grating?
Where the concrete surface and brick wall meet there appears to be a sand and cement fillet - is this the case?