The letter, sent to the assembly's transport committee, said: "I would ask you to give serious consideration to exempting those commercial vehicles that have no choice other than to enter the congestion charge zone on either a temporary or permanent basis."
Ankers said the letter asked the assembly to consider the effect the charge had on business before extending it outside central London.
He said: "Our members cannot choose whether or not to enter the congestion charge zone when delivering products to sites in the zone."
Ankers cited figures from a recent joint survey of CPA and Construction Confederation members that revealed that 80% of manufacturers and 83% of contractors have suffered a rise in costs as a result of the charge.
The survey also showed that almost 60% of those surveyed had seen no benefits, in terms of ease of deliveries, since it was introduced.
Building launched its Chop the Charge campaign in February in an attempt to obtain an exemption from the charge for the construction industry.