I know controllers have several short shifts each day with interval breaks but I was wondering how many planes they assist in taking off/landing depending on what type of controller they are each day? Locational wise perhaps LHR? (London Heathrow)
From the title of your question (taking off / landing planes), I assume you are asking about a tower controller. As you may know, most air traffic don't work in a control tower, but are en-route controllers working in an ACC (area control center).
The number of planes a tower controller handles each day is of course highly dependent on the airport traffic conditions (november, for example, is a quiet month). I work in an European single-runway airport, where the runway capacity is 40 flights / hour (landings and departures included) in optimal conditions. Controllers usually work around 5 effective hours per day, so the theoretical maximum number of planes would be 200 planes. In practice, it is very unlikely that a controller will actually control that number of aircraft, because the runway is used at maximum capacity only during peak hours (early morning, late afternoon and beginning of the evening). Also, a tower controller doesn't only work at the tower position, she will also be typically work a clearance delivery and an approach position.