Blocked drains inside the building should be reported to the managing agent in the usual way unless they are internal to a flat, in which case you can deal with it yourself.
However unfortunately the drains often block outside the building; underground. These drains are the responsibility of Thames Water and you can telephone them to come and unblock them. They usually respond fairly quickly. Maybe one day they will realise that it might be better to dig them up and re-lay them.