Yes you can, but if you are quite capable of doing it yourself, or ask too often, you might pee him off a bit. I'll do it for the old dears or if I like someone and IF I am passing a box or IF I am going back to the sorting office after delivery, which I don't always do.
It is a sackable offence for a postman to have any mail other than personal mail or mail for delivery on him, so if he refuses, it could be because they are not going near a box or retutning to the office, and you can't blame them for playing safe.
I have to be honest, since the one delivery was introduced, the need to return to the sorting office when you take out a delivery has reduced quite a lot.