Loose handrail

My handrail is coming off at the bottom of the stairs. I’m debating what to do. I think the plaster has crumbled under the force of me holding on to it, it has been a bit damp there so it could be that which has caused it.

Anyway I’m going to try using a strong adhesive. Possibly by glueing the rawl plugs in place first, then using it to glue the plate in place and screening up the screws back into the wall. Does this make sense? Fingers crossed!