Remote hunting for ladybirds in Singapore is proving both interesting and frustrating. A search for 'ladybird singapore' on Flickr provides lots of hits, for example. This can give some clues about where and when to look for these beetles, but not necessarily the name of the species found.
The examples uploaded to Flickr for ladybirds do not look similar to the species found in the United Kingdom. I am guessing that there would be more of an overlap with the ladybirds present in Australia. That could be helpful as there are efforts, in the 'Atlas of Living Australia' to map the presence of ladybird species there. Another site interested in of ladybirds present in Australia is 'Ladybirds of Australia', especially the Image Gallery.
One ladybird that seems to be present in both Singapore and Australia is Harmonia testudinaria.
One was seen on March 8, 2008 in Choa Chu Kang New Town, South West, Singapore. It has been mapped across Australia in the Atlas of Living Australia.