How and when did the British surrended

They were defeated by a lack of tanks, losing air superiority and a series of Japanese flanking movements along the coast (the Royal Navy in the area having been effectively destroyed by air attacks). Even the big guns in Singapore were unable to effectively support their troops having too few high explosive rounds, they were supplied with plenty of armour piercing ammunition which is less effective against infantry.
Adapted from : http://au.answers.yahoo.com/question/index?qid=20101114021043AA8Y5O9

Why did the British surrender in Singapore?

The British & Commonwealth forces surrendered at Singapore largely because of the swiftness & surprise in the attacks by the Japanese in the Malay peninsula. Hugely stretched by the potential war in Europe & the actual war against the Axis in North Africa the British lacked the resources to defend the Far East against Japanese aggression. With hindsight it might be argued that surrender was premature, but even then defeat was surely inevitable in the longer term. Had the Japanese attacks not involved the US, brining them into both the Pacific & European conflicts, then Britain & the Commonwealth are under the sort of pressure which may have become intolerable.

The Japanese actually tricked Singapore by lying that a huge troop of Japanese would come and attack Singapore the next day if the British did not surrender. However, the Japanese actually did not have that big troop of army and their supply of necessities were depleting. If the British did not surrender, the losing side might be the Japanese instead.