By LAUREN WELCH & Mariam Khan Prince Harry did not see his father during his whirlwind trip to the UK this week, but a royal expert believes a reunion is on the cards – on two specific conditions. The Duke of Sussex flew into London on Tuesday ahead of an appearance at St Paul’s Cathedral the following day, sparking rumours he might be meeting up with King Charles. The relationship between the two has been frosty in recent years, particularly following the release of Harry’s tell-all memoir Spare. However Harry didn’t stay in the UK very long and is already in Nigeria promoting the Invictus Ga…