By Dasha Afanasieva LONDON, Jan 8 (Reuters) - British firms grew more confident in the last three months of 2012, suggesting the economy avoided contraction and is set for modest growth in the early part of this year, Britain's largest business survey showed on Tuesday. The survey of more than 7,000 firms by the British Chambers of Commerce contrasts sharply with the downbeat message last week from a set of closely watched polls of purchasing managers. They suggested Britain is slipping back into recession.