We've seen this before: wanting to travel off-season for budget reasons often hits a wall when you have school children.
Historically, school holidays in the UK are fixed and fall during peak periods, making the concept of "low season" almost irrelevant for families.
Trying to shift a trip for lower fares is a lost battle that doesn't take into account the practical realities of family life.
For example, trying to leave in November to avoid summer prices often means missing school, which is unacceptable, or facing terrible weather that ruins the stay.