The latest drive coincides with a petition on the Number 10 Downing Street website that asks the Government to drop the tax.
The petition, which has more than 2,600 signatories, says repairing listed buildings has become uneconomic because it incurs VAT, whereas demolition and rebuilding do not.
"Fiscal policy is encouraging the destruction of well-loved and historic buildings and encouraging their replacement with inferior and often shoddy new-builds," said the petition's creator, who claimed to be a representative of Birmingham City Council.
Kate Pugh, secretary to Heritage Link, an umbrella body for heritage charities, said that dropping VAT would enable charities to pursue their primary objectives.
"If almshouses, which are often listed buildings, didn't have to pay VAT on mending their roofs, they could spend more on their social missions," she said.
A spokesman for the National Trust said: "We have long felt there is a discrepancy with the issue of VAT on repairs of listed buildings, and we would encourage the Government to look at it again."
The petition, available at http://petitions.pm.gov.uk/NoVAToldBuildngs/, is to close on 31 January.