In the past few years, LBS has become one of the main schools for those targeting consulting after the MBA (or even in an entry level).
LBS has direct contact with some of the main firms, specifically with the London offices which a lot of times serve as hubs for other offices around the world. Also, LBS's career centre puts a lot of attention in recruiting for consulting. There are ~3/4 people solely focused in consulting, with a very significant industry expertise that can help you guide your search and preparation. The school offers various courses that enable you to have a real life experience in consulting, like London CAP where you work on a real life project helping a company. And lastly, there are two student led clubs fully dedicated to consulting (the Consulting and Impact Consulting Club). Both clubs are very active in the LBS community and outside, with partnerships with various firms and organizing case competitions, for example.