(Fixes typo in headline)
LONDON, Jan 4 (Reuters) - Sterling inched higher against a broadly weaker dollar on Wednesday, with solid indications of business and consumer sentiment helping pull it back from two-month lows hit on a volatile first day of 2017 trading.
The early departure of Britain's ambassador to the European Union, and the tone of his resignation letter, have added to concerns of a rocky few months in prospect for sterling as Britain prepares formally to launch talks on leaving the bloc.
But data on the economy itself remains far stronger than many economists feared after the vote for a Brexit last June, and construction industry and consumer credit data on Wednesday both beat forecasts.
Tuesday's survey of factory purchasing managers also showed manufacturing growth hit a 2-1/2-year high last month.
"Other sectors have already predicted increased prices and trimmed forecasts for the months ahead due to a weak pound, but the all-important construction industry seems to have avoided the same fate," said Dennis De Jong, managing director at online currencies broker UFX.
"With Article 50 due to be triggered in a few months' time, uncertainty will surely affect the construction industry for the foreseeable future. Long term planning for construction projects is sure to become more challenging, but today's data indicates a solid foundation remains."
Sterling gained 0.3 percent on the day to trade at $1.2276 after the numbers and was steady at 85.02 pence per euro, down from a two-week high of 84.51 pence on Tuesday.
Politics are widely expected to weigh on the pound at least until the promised formal start of exit talks with the EU's 27 other members in March.
In his letter to staff, outgoing EU ambassador Ivan Rogers called on colleagues to challenge "muddled thinking" and said that Prime Minister Theresa May's objectives for Brexit were still unknown to her government's representatives in Brussels.
"I don't think any of that story can be positive for the currency. It highlights the uncertainty that has weighed on sterling for some time," HSBC strategist Dominic Bunning said.
"It is not a massive new reason to sell cable and was probably offset by the positive economic data we got yesterday. But the gains in the past few hours are really just a dollar move." (Editing by Catherine Evans)