22 December 2015 Last updated at 11:22 GMT
The two male suspects are believed to have scaled a fence in the back garden and broken into the house in Ashbourne Road, Mitcham, sometime between Saturday morning and Monday afternoon when the theft was discovered.
The thieves damaged cuddly toys, puzzles and games belonging to the victim's' baby and stole gifts including jewellery, photographic equipment, a tablet and a laptop computer.
CCTV footage has been released of thieves stealing gifts from under a Christmas tree at a home in south London.