Forget the embassy*. Embassy generally only offer assistance when one of their citizens/nationals has become the victim of a crime or if there is a crisis (natural disasters, civil unrest, war, etc.). They often intervene as liaison when a citizen is arrested, has been attacked, hospitalised in a critical condition and no next of kin is with that person, or has died.
@OP, surely you have a friend, a relative or colleague that could advance the £100 to change your flight?
*Unless you have been victim of an actual crime and there's absolutely no other alternative.