This is, I’m afraid another of the myths told regarding the fall of Singapore.
Although the northern shoreline of the island was primarily mangrove swamp, that didn’t prevent the construction of the naval base at Sembawang, which was on the north shore of the island.
The truth of the matter is that there was never any attempt to construct defences along the northern shoreline.
Ivan Simson, formerly the Chief Engineer of Malaya Command, arrived in Singapore on 5th August 1941. Being an engineer, part of Simson’s duties were to plan and construct defences that would stop or slow down any attacking forces. According to Simson, he examined the records of his predecessor and saw that he had been unable to get approval to start constructing major defences on the north shore of Singapore Island. Simson then developed a series of proposals for fortifying the north shore and arranged a meeting with General Percival, the commander of the British forces. According to Simson, Percival rejected all his proposals without giving any reasons. Simson then contacted his superiors in London to see if they could force Percival to authorise the construction of the appropriate defences. The High Command in Britain never took any action in reply to Simson’s appeal for help.
The construction of adequate defences along the northern shoreline would almost certainly have slowed down the Japanese advance. However I doubt that they would have done any more than delay the inevitable defeat.