British forces will wrap up their mission in Iraq in the first half of next year, British Prime Minister Gordon Brown said during a surprise trip to Baghdad on Wednesday. "By the end of May, or earlier, the mission will be completed," Brown said at a joint press conference with his Iraqi opposite number Nuri al-Maliki, adding that the troops would go home over the following two months. Brown is on his fourth visit to Iraq since he took office in June last year, hot on the heels of a farewell trip by George W. Bush that was marked by an Iraqi journalist hurling his shoes at the US president.