Borough market has to be one of my favourite places in London. Over the years it has undoubtedly become a massive tourist attraction and is generally packed, especially on the weekend. I would avoid Borough market on the weekend if you can. The market is open from Wednesday to Saturday (included).
The market is one of London's most renowned food markets with product from all around Europe. Truffles and cheese from France, the most amazing selection of ham and salami from Italy, olives and spices from Turkey to Greece...
I do have to warn you that you will probably end up spending a fortune as everything looks, smells and tastes amazing but it also all comes at a price.
Although they say that the market is a dog-free zone I always go with Lemon and we have yet to be told otherwise.
8 Southwak Street