I would be very surprised if the estate agents agreed to this. They only collect rent on behalf of the landlord, who will probably have a mortgage to pay so is unlikely to agree. I know as a landlord I would never agree to an arrangement like that.
Being a landlord as well I would not be happy with this either, my rental people have been a week late before and it has a big impact on how I deal with my own finances.

Unfortunately I know that they places like My Budget (in SA) and similar agents some of the first payments they delay ARE rent