Titan Tours would probably try to switch your flights to another carrier if there was a problem with BA. However their booking terms contain a 'force majeure' clause, as follows;
"Force majeure - This means that we will not pay you compensation if we have to cancel or change your travel arrangements in any way due to unusual and unforeseeable circumstances beyond our control the consequences of which could not have been avoided even if all due care had been exercised which includes: war, threat of war, riots, civil strife, terrorist activity, INDUSTRIAL DISPUTES, natural or nuclear disasters, fire, adverse weather conditions including hurricanes, epidemics, health risks, unavoidable technical problems with transport, closed or congested airports."
Chris