The tower is the Elizabeth Tower, so Large Liz might be appropriate. It's been this way since Lizzie's Diamond Jubilee (it's a Brit thing) in 2012.
Big Ben is the largest bell in LL which was often confused for the tower itself, with much media calling the tower Big Ben when it was actually St. Stephen's Tower, or Sizeable Steve
You can call it whatever you want, but you'll have to explain you mean Big Ben, the giant clock tower unless your friend is up on recent Westminster history.