When a modest IT firm in southern England won a 13-million pound local authority contract in 1988, it was a huge coup for a business that had annual revenue of just 4.3 million pounds.

Nowadays that company has annual revenue of 3.4 billion pounds thanks to its dominance of the public sector services market – and Britain’s government thinks it’s time that Capita (CPI.L) returned some of that business to smaller firms.

“We have an oligopoly,” said Bill Crothers, the government officer charged with overseeing all central government contracts. “We have a huge concentration of business in relatively few suppliers.”

Outsourcing public sector services to private companies has been a controversial issue in Britain since former prime minister Margaret Thatcher introduced compulsory competitive tendering in the 1980s. That forced local authorities to give private firms the chance to run everything from councils’ IT systems to hospitals and rubbish collection.

As a result the public services market boomed and is now worth 93 billion pounds, according to figures from market analyst Kable. That makes it second only in size to the U.S. market, says data analyst Information Services Group. Capita, along with Serco (SRP.L) which runs NHS health centers, enjoyed double-digit growth for two decades until the current austerity-focused coalition government was elected in 2010.

Now outsourcing is controversial again, with a recession-weary public quick to get angry about private sector payouts given curbs on welfare spending and bleak growth forecasts.

So David Cameron’s government is taking aim at the big contractors to both answer voters’ calls for a fairer marketplace and to boost the economy by passing more money to small and medium-sized companies (SMEs) – those with fewer than 250 employees and a turnover of less than 50 million euros.

Cameron terms SMEs the engine of economic growth and wants them handling 25 percent of all government contracts by 2015.

Even Rod Aldridge, co-founder of Capita, says change is due. SMEs can’t compete in the current climate given the 25-year-old relationships built up between bigger firms and local councils.

“The industry has now got a problem,” said Aldridge, who now runs an education foundation. “Lots of small specialists..can’t bid for some of the things which are out there. The government is worried because you haven’t got competition.”