In fact the maximum draft at Fawley is no more than around 15m dependent upon tide with maximum displacement of around 240K tonnes. So a fully laden VLCC would never get in there anyway discharging often first at Rotterdam or Antifer. Afraxmaxes of around 120K tonnes can come in fully loaded (again on the tide).
There are also, as mentioned, draft restrictions in & around the deep draft channel which is a pain especially during Cowes week when the old adage of 'sail gives way to steam' is taken literally by some 'weekend' yacht people who think they can force a tanker to give way at a moment's notice.
But the cross-currents just south of Calshot can cause some problems as I mentioned earlier..
John