For just a wipe-down, a damp cloth will do it. For larger, deeper cleaning...
There is a line of leather-cleaning supplies from a company called Lexol. They have been working with leather for several years.
A saddlesoap (Aussie's is pretty good) is also a good bet, but it also depends on what TYPE of leather your shoes are made from! Suedes will react differently than the leather used for tennis shoes or car seats.
Your best bet, since these ARE Burberry shoes you're talking about here, might be to take them to a shoe repair. They should be able to clean them for you, or direct you to the perfect product!