A week involving new year is probably going to be the most expensive week of the year for holidays due to a number of factors:

- Massive demand over a week or two week period
- Limited destinations offered - destinations such as Greece and the Balearics aren't offered over Christmas, meaning that demand is going to be centered around fewer destinations.
- Aside from being a hugely busy period, the Canaries are also the most popular short haul destination of the Winter.
- In the days of high oil prices, airlines feel they can't afford to have flights with empty seats, meaning they will offer far fewer seats than are in demand to ensure they are filled. It also gives them an excuse to charge more.

Ultimately, for peak travel periods such as Christmas and Easter, you should book as early as possible, which for this New Year would have probably meant last November/December. Your best bet would be looking at flying from Manchester, where there will be a great deal more flights. I have just had a quick look on Travel Republic, and the cheapest they were offering from Newcastle for flights to Tenerife on the 26th Dec was £500, whereas from Manchester it was £388. Still expensive, but for a family of four, a saving of £448.