If no interview is required, 10 working days max, probably less.

If an interview is required then as interviews are held on a strict "first come, first served" basis it could be up to 16 weeks. However, as your step-son is only 5 it is almost certain that they wont want to interview.

10 Working days seems a long time i was expecting 3 to 4 days

Would a postal application speed up process?

10 days is a conservative estimate, the application centre website actually says 2 to 5 days and some people have reported a 24 hour turnaround.

Nothing you can do to shorten the time, it all depends on how busy they are. Posting it will only take longer, as they cannot begin to process it until they have received it.