If you don't use a flash, the pictures can have almost no color. Even if you enhance the brightness later, it probably won't look good.
But if you do use a flash, you'll probably get the Martha Stewart problem where the flash adds blues and greens to the images, wrecking the color of the food and making it incredibly unappealing.
Food is probably the single most unforgiving subject for low-light photography. The reason is that a good photo needs to look appealing to the viewer. Color is one of the main cues our brains look for in food to determine whether it looks good enough to eat, or is best left alone. If the colors are off, turned grayish by darkness or greenish by flashes, there's often no way it can look edible.
Another option is to buy an iPhone 5S, which has a color-correcting flash. It can detect how off-colors may wreck your shot, and it changes the color of the flash itself to compensate. This helps, but doesn't always solve the flash problem.
Nigella Lawson's bad food photos have two problems. First, they tend to be out of focus. This may also be caused by low-light conditions, as most smartphones focus more slowly in low light.
The solution to this problem is to use your smartphone camera app's "select focus" feature, which lets you tap on the screen to tell the software where the camera should be focused. If you don't have one, then just do your best without it. Also: Take several shots -- five or six might do it. Chances are at least one of them will be in focus.
Lawson's other problem is that she tends to cast a shadow over the food, which will usually ruin a food photo.
In general, favor diffused natural sunlight or bright ambient light. Most of all, if your food pictures look bad, don't post them!
Another major tip: Use Google+!
Unlike the other social networks, Google posts your pictures at full resolution (Facebook and other social networks compress photos, degrading their quality). Just uploading pictures from your smartphone (which can be done automatically) will run them through Google's incredible photo editing tools that automatically improve food shots without any action by the user. These automatic editing features actually detect that your picture is of food, and will apply conservative improvements that boost the color in the right way, compensate for the flash and do other things that would normally require skill and experience with a photo editing tool. Google+'s built-in manual tools can make photos look even better.
Even if you choose to post on other sites, like Facebook or Pinterest, I recommend running photos through Google+ first. Simply install the Google+ app on your phone and set up Auto Backup (which uploads your pictures to a private area -- they won't be shared until you share them). If you want to post your pictures on another site, just use the menu option on Google+ (when you're looking at the photo) and download them, then upload them to the service of your choice.
Sign up for CIO Asia eNewsletters.