Sub question: When I lived in Singapore the answer given to this question by colorful storytellers was usually that the British were prepared for a naval invasion, so all their artillery was directed outward and the Japanese traversed through jungle and even rode bicycles to surprise the British forces from the rear. Is there any truth to the Japanese forces actually riding bicycles during their attack? (or troop movement)
While the British and Commonwealth forces (primarily Australian and Indian regulars, on top of volunteers levied from the Straits Settlements itself) indeed outnumbered the Japanese army, there were several key disadvantages which I hope to raise.
The first was some element of surprise and lack of preparations. The British definitely expected a Japanese invasion of the region; Singapore, in particular, known then as the 'Gibraltar of the East' for its immense strategic value as the largest Royal Navy station in the far east, was almost certainly going to be a target. However, what the British were less sure of in general was how this attack was going to unfold. The prevailing thinking at that time amongst top military leadership was that the Japanese would attempt a naval assault from the east, possibly from staging areas in the south of the occupied Philippines. As such, a significant of British heavy guns and defensive emplacements were in the southern and southeastern coast of Singapore, pointing towards the sea. (Many of these fortifications, such as Fort Siloso and Fort Labrador, remain today although they've been converted to civilian uses or as tourist spots.) Not much thought was given to the Japanese attacking from the north instead, by following downwards the Malayan Peninsula because the British did not think that any invading force sufficiently large enough to conquer Singapore could manoeuvre that much men and material through the dense jungles of the peninsula without being bogged down or worn out by the heat and disease. For this reason as well the British in Singapore did not have tanks, because they did not think armoured vehicles would be practical in the jungles or the narrow, muddy roads that snaked through them. The Japanese did exactly this, moving large numbers of soldiers on bicycles that could easily negotiate the jungle paths. The invading Japanese army consisted of well-trained crack troops, veterans from the Manchuria campaign when Japan first invaded China in 1937. Furthermore, a good number of its leaders and officer corp received rigorous training at the specialised jungle warfare schools in occupied Taiwan. In terms of fighting quality and overall morale, therefore, the Japanese army was in a much better position compared to the British/Commonwealth garrison, most of whom were either fresh recruits levied quickly across multiple colonial nationalities to meet the rising threat in Asia with little training and little integration (linguistic barriers were a problem, and while doing research for a paper I wrote on this topic I've read anecdotal accounts that the British pilots and Australian pilots in Singapore often fought with one another, while British officers found it difficult to communicate with the rank and file of Indian and Malay soldiers. While it is not clear that these disagreements eventually translated into poor combat performance or not, it does highlight how fractious the garrison was in Singapore even before the first shot was fired). Note: One common misconception that is often repeated, especially in the Singapore history curriculum (at least when I was studying) and popular imagination, is that the British guns were 'pointing the wrong way' and thus completely useless when the Japanese invaded by land instead of by sea. This is not entirely correct, as the gun emplacements could be traversed 360 degrees and were traversed to meet the incoming threat. The bigger problem was that they were largely calibred with armour piercing rounds designed to penetrate the armoured hulls of Japanese warships, and not conventional explosive rounds which would have been mot effective at repelling infantry attacks.
The second factor I'd like to argue for is the lack of fighting supplies and resources the garrison in Singapore had access to. Remember how I mentioned that conventional military thinking amongst the British predicted a seaborne attack? Not everybody felt this way. For example, Lieutenant-General Arthur Percival, who was in charge of the defense of the Straits Settlements, believed that the Japanese could very well invade Malaya and then move south to Singapore by land. A plan titled Operation Matador was drafted for the pre-emptive invasion of neutral Thailand by British forces to secure potential Japanese landing sites. But this plan never materialised, most crucially because the British in Singapore lacked the resources to mount such a large-scale move, and the military leadership felt it was best to conserve said resources and defend prepared positions along the peninsula and finally in Singapore itself. The crippling effect of insufficient fighting material was by no means limited to this example alone--in fact, it was a repeated trend. At the 1941 Arcadia Conference, Prime Minister Winston Churchill and President Roosevelt agreed on the 'Germany first' policy, committing the bulk of their military efforts to winning the European war against Hitler's Germany first, before turning their sights to the Asia-Pacific. In retrospect this was a completely understandable decision, in 1941 the Britain was practically alone in its resistance in the Western European theatre, and I think naturally would have prioritised the survival of the national homeland over colonies in the Far East. In any case, the consequence of this decision was that Singapore received very little outside support in its defense. Task Force Z, a naval battle group which was dispatched to defend Singapore, was so depleted and under-strength that its two capital ships, the HMS Prince of Wales and the HMS Repulse, were quickly overwhelmed and sunk by Japanese dive bombers without having made any real contribution to Singapore's defence. The Royal Air Force in Singapore flew outdated and poorly maintained Brewster Buffalos which were more than outmatched by the faster and more numerous Japanese Mitsubishi Zero fighters. The much more adept British Hurricanes and Spitfires, made iconic by the Battle of Britain, were largely reserved for fighting in Europe. For the length of the battle of Singapore, the Japanese practically had unchallenged air superiority. Commonwealth ground troops were not equipped with anti-tank weapons because armoured forces were not expected to have made it past the Malayan jungle. Ultimately, what drove Percival to surrender in February 1942 with the bulk of his forces intact was the lack of essential supplies. When the Japanese captured the central water catchment areas in Singapore, they were only weeks from running out of supplies and ammunition, but the British supply situation was much worse. Hence, short of water, medicine, and with a severely demoralised force, Percival decided to surrender instead of holding out for a final confrontation in the city.
Edit: Tagging u/thesilverpig since this may answer some of your questions in the other comment! In particular I think you'd be interested to know that (a) the British naval guns were pointing seaward but could be traversed to face north, and (b) the Japanese did move most of their infantry on bicycles, which proved very effective in navigating the dense Malayan jungle.
Hi, I am a bit late in answering this as I have been busy but you can take a look at some of my previous answers if you are interested.
This is on the general reasons why the British were defeated.
u/thesilverpig , again apologise for the late reply, this is an answer I did on the use of Bicycles by the Japanese.
To just quickly answer your point on their naval fortifications, yes they were more well prepared for a naval invasion with the main bulk of Singapore's static defences being large naval gun emplacements. Many of these guns were trained to fire on Johor once it was apparent the Japanese weren't going to launch a naval invasion of Singapore so they weren't entirely useless. However, these guns were armed with Armour Piercing shells for use against ships and were fairly ineffective against Japanese troop concentrations across the straits of Johor since High Explosives were normally used against land targets.
If you have any additional questions do feel free to let me know. u/slumberjackbear as given a pretty good account of what happened already and covers the lesser known points like Ops Matador. Although I don't think I fully agree with the point on lack of supplies in general, although there was a lack of modern equipment, I was definitely a major problem towards the end of the campaign after they had exhausted many of their stores.