"If Britain gets our taxpayers, shouldn't it also pay their benefits?" Sikorski asked in an English-language comment on Twitter. "Why should Polish taxpayers subsidise British taxpayers' children?"
Cameron announced last month that a British crackdown on "benefit tourism" would begin on January 1 when migrants from the European Union will be banned from claiming unemployment handouts until three months after arrival.
He spoke after pressure from his Conservative party and right-leaning newspapers to manage an expected influx of migrants from Bulgaria and Romania, two of the EU's poorest members, when restrictions on their entry to Britain end with the start of this year.
"Britain earned a lot (of money) on Poles finishing off communism, he (Cameron) shouldn't forget it and he should tally it all up," Walesa told AFP at the end of last month, pointing to the economic boom sparked by the reunification of Europe after the demise of communism in 1989.
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"Then he would understand that countries like Great Britain are once again behaving unreasonably and shortsightedly," he said.
Under tightened migrant benefit rules adopted by Cameron's government, migrants will not receive out-of-work benefits for the first three months in Britain and payments will be stopped after six months unless there is a "genuine" chance of them getting a job.
The biggest group came from Poland. Around 640,000 Poles live in Britain, according to official statistics released in 2012, but the Polish community estimates the real figure might be as high as one million.