Optimism is creeping back into Britian's smaller firms as many expect output and domestic orders to pick up in the three months from January, according to a survey by Britain's biggest business lobbyist the Confederation of British Industry.

This is despite smaller firms reporting a decline in domestic and export orders in the three months to January, as the depressed economy muddled through yet another contraction of GDP, which slumped by -0.3 percent in the fourth quarter of 2012.

"Activity has continued to contract this quarter, with falling production disappointing growth expectations," said Anna Leach, CBI Head of Economic Analysis.

"Nonetheless, better news on the domestic front is expected, with output and domestic orders set to rise modestly. But there is little sign of improvement in export prospects, and uncertainty over demand continues to weigh on investment plans."

There was a +9 percent balance from the survey's 347 respondents on expectations of total new orders growth over the coming three months.

However, this will be solely driven by domestic orders - with a positive balance of +10 percent - as new export orders are expected by most to continue falling, with a negative balance of -2 percent.

A global downturn - with slowing growth in emerging markets, no resolution to the eurozone crisis, and fiscal concerns in the US - is weighing heavily on the UK's export market.

Chancellor George Osborne has set the Treasury a target of increasing the total value of Britain's exports to £1tn by the end of the decade.