Living in Singapore, I get my meat from the wet markets or direct from the farms located in the far flung corners of this island. However, a more convenient & reliable alternative is required for everyday and for that there are online butchers. Most butchers are specialists and offer prime cuts of meat at premium prices, but there are some that do offer economical prices.
List of local butchers:
www.temasik.com (wet market)
For fresh vegetables, try bestorganicfood.sg that carries cheap organic vegetables or just grow your own (buy seeds from buyseedsshop.com).
* Only local sites are listed here!
** Pictures from etour.com