Tax breaks did not create a faster British merchant fleet

Would an official British program to replace merchant losses with modern ships have improved Second World War convoys?

Only with stronger direction; the actual tax incentives mostly produced cheap replacement tonnage rather than faster ships.

Britain had a limited official effort to encourage replacement merchant construction. Tax relief encouraged owners to build ships, without concentrating the program on better vessels. Owners generally chose inexpensive replacements. Producing more modern ships for fast Second World War convoys would therefore have required incentives directed toward improved capability.