Mrs Armstrong said that Britain's most efficient local authorities should be rewarded with the power to raise their own cash, but the Conservatives and business groups immediately condemned the plan as a "back door tax" that would cripple small firms.
Only those boroughs with a proven record of providing high quality services will be given the power to levy the extra charge on top of the existing national business rate.
Beacon councils will have to show that they have turned around failing schools or offered residents other outstanding "bread-and-butter" services such as refuse collection and home repairs.
Simon Burns, the Conservatives' environment spokesman, said that the idea of a new local business tax would horrify most firms. "Businesses both small and large would suffer from having to bail out councils. This takes the gloss off [Labour's] attempt to portray beacon councils as centres of excellence. It is a quite disgraceful idea," he said.
Andrew Hawkins, policy director of the London Chamber of Commerce, said: "We have great concerns about this. Councils have been dying to get their hands on the business rate again, but we believe that no local rate should be set unless more than half of the firms agree to it in a referendum. No taxation without representation, is our stance.
"It may appear to be a modest top slice, but we calculated recently that a company could face a pounds 10m rise in rates for every 1 per cent rise in the business rate across the UK."