Free food in Central London is surprisingly easy to find. If you are out late at night, there are a number of "soup runs" and "tea runs" which offer free soup, bread, tea and sandwiches, with some of them offering more lavish sustenance and even free hot meals at times. There is even a "hot chocolate" van that offers steaming hot cups of chocolate!
A good way to link into the network of knowledge for these free food offerings in London is to join the homeless in The Strand any night after midnight, or earlier in the evening at Lincoln Inn Fields at approximately 6pm - you will see other people congregating for free food. You will find out times, venues and tips for free food in London from people who are actually using the services.
Other good venues for free food from the soup runs are Temple Gardens, Embankment, Howick Place in Victoria and Lincoln Inn Fields, most nights from 6:00pm.
Many charities and homeless drop-in centres publish lists of free or low cost resouces. Try any citizens advice centre for information. You do not need to give your name when requesting information so you can remain fully anonymous.