Bottom line is:
1. A week in Turkey for a family of 5 can be found at a cheaper price than a week in many UK holiday parks.
2. It's cheaper to pay the fine for taking kids out of school than it is to go on holiday during half-term and summer holidays.
3. When you look at the areas many of these families live, their cost of living is a lot less then many others. That coupled with years of being thrifty, shopping for much less, buying cheap, maybe not having to pay for cars, no subscriptions, etc, etc, means that many are capable of putting money aside or booking a year, 2 years in advance and paying in small sums. There's loads of travel agents around offering payment plans, and those payment plans are there to offer people an opportunity to go abroad for a week, so they take it.
It's very easy to assume that people are affording themselves things that should be impossible on benefits. If person A. pays £4,000 for a family holiday in Turkey, there's a high probability that they will sit on the beach next to person B. who paid £1,500 for a week in the same part of the world.
A question you should be asking is why do you pay so much to travel away for a week when somebody else did it for at least half the price.
Also, if you're willing to pay a good year or two in advance, if available, flights can cost 50% less than in the last few months before the departure date. Trust me, I see it all the time.
In the past couple of years I've paid a total of £1,200 for direct return flights to SeaTac, for 3 people, that only 6 months later have increased to £2,900.
If you use your head, you can travel for a lot, LOT less than the next person you find yourself talking to at the beach.