The association attended a meeting with TfL today (17 March) in which it said the transport body estimated that of the 188,000 HGVs operating in the capital, 35,000 would be banned from London by 2020, rising to 94,000 by 2024.
The standard, first announced last September, will assign HGVs star ratings based on in-cab visibility.
Only those with the highest rating will be allowed to enter London when the proposed legislation takes full effect in 2024.
RHA chief executive Richard Burnett said: “This is a fiasco - it is shocking attack on business in the capital.
“The cost of this will be met initially by road hauliers, but will eventually be picked up by the people of London.
“Businesses and people depend on lorries to deliver the goods they need, including the food we eat.
“It seems TfL is determined to undermine the competitiveness of London. The timings and requirements that are being specified are ridiculous.”
Burnett added that with restrictions on vehicle emissions also to contend with, TfL’s standards are “impossible” for operators to comply with.
“It’s impossible for a haulier to buy a vehicle now that complies with TfL standards as no vehicle has been assessed against any standard,” he said.
“It is absurd to expect businesses to invest many tens of thousands of pounds in new, clean Euro-6 vehicles only to have them banned by TfL in a little over two years' time.
"Of course we understand the need to make the roads as safe as possible, but this proposal has run off the rails. It is simply not credible.”
TfL queried the RHA's figures from the meeting, but did not respond to requests for further information.