The problem was nobody expected Singapore to fall, so there was no rush to create an evacuation fleet. To the contrary, Wavell was arranging a reinforcement convoy for Singapore. By all rights, Singapore shouldn't have fallen, but it was another example of shockingly bad Army leadership. Lt-Gen Percival simply wasn't up to the job. Whilst he had a record as a brave captain in WW1 (he won the MC), he was a favourite of staff officer General Sir John Dill, and it seems he was promoted beyond his ability due to favoritism. In the event, Percival proved he was another staff officer that was good on paper and cr*p in the field.
Arguably, Percival's biggest failure was that he noted the poor defences of Singapore from mainland attack as early as 1937, but did nothing about it other than write another ignored report. Percival then sat on his hands. He was notoriously unimaginative, doing so much by the book that he banned his troops from practicing jungle fighting as the predominant staff idea of the day was that the Malayan jungle was "impassable" to troops. When the Government only allocated 60,000 pounds to building defences on the landward side of the island, not only did Percival not question this, he did not think of inventive ways to use the manpower and materials available to him to build more defences. Compare this to Malta during the same period, where troops were not just used to build their own emplacements, but also used to repair runways, help refuel/re-arm aircraft, dig shelters, carry ammo for the AA, and even offload supplies from ships at the docks. Troops stationed on Singapore square-bashed and sunbathed even whilst their colleagues were being driven down the Malayan Peninsula by the Japanese.
Unfortunately, when fighting in Malaya did start, the Japanese found Percival as predictable and unimaginative as his own command officers did. By the time Wavell arrived in January 1942 it was too late, and he promptly ignored Percvial for the advice of a more junior officer he knew. Things got worse because Wavell correctly predicted the Japanese route of attack and even the exact place they would attack Singapore. Percival simply went his own way, probably because he thought Wavell was going to sack him anyway. Whilst Wavell had managed to get the RN to commit to a relief fleet (not evacuation), it was predicted to be 70 days before it could be in place. Percival then doomed Singapore in seven.
It might have been possible to mount an evacuation of Singapore if equally poor Naval leadership by Admiral Phillips hadn't already cost us the loss of Force Z, but the RN was so traumatised by the loss of Force Z that they convinced themselves that the Japanese fleet and bombers were just waiting for the RN to send a fleet up to Singapore, hence their insistence on the 70 days to get a relief fleet assembled.