A typical black cab is licensed to carry up to five passengers. But two of those seats are "fold down" affairs that face backwards. The vehicles have some space for luggage in the front of the cab (there's no front passenger seat). You could fit a couple of suitcases in the back too.

Probably cheaper and more comfortable to pre-arrange a pick up in a van: http://www.addisonlee.com/services/minicabs/