On what day of the week? Are they citizens of a nation outside the EU? What class are they flying? If they are non-EU citizens flying anything other that first class, it may take them 2+ hours to clear immigration at LGW, so the earliest Gatwick Express they can catch would be the 1050 that will put them into Victoria Station at 1120.

As the Mounting of the Guard at the Lifeguards barracks is at 1100, I would say the odds are very long that they will make that on the first day in London.