As EC states, flights to the Canary Islands are always really expensive around Christmas. It's the ONLY warm destination within a short travelling time from the UK. (To find some warm sunshine anywhere else you've got to consider places like The Gambia, the West Indies or Australia). In consequence of that, there's massive demand for flights and airlines can sell nearly all of their tickets at full price.
There are four airlines that operate direct scheduled flights from Gatwick to Fuerteventura. They are Thomas Cook, Thomson, easyJet and Monarch. If you've tried those four airlines, that's it.
Thomas Cook only fly that route on Saturdays and Wednesdays. Out on Wed 19/12 and back on Boxing Day costs £285.98 per person. There is no availability outbound on Sat 22/12.
Thomson also only fly on Saturdays and Wednesdays but, once again, they don't offer outbound travel on Sat 22/12. That just leaves outbound on Wed 19/12 and back on Boxing Day for £323.98 per person.
On those same dates, easyJet is offering a return fare of £295.25. Yet again, they only fly on Wednesdays and Saturdays. Outbound travel on Sat 22/12 is available (coming back a week later) but at a much higher price (£553.43 per person).
Monarch appear to suspend flights to Fuerteventura from Gatwick over the winter months. The only flights offered on their website depart from Birmingham or Manchester.
So (if you're prepared to fly back on Boxing Day) Thomas Cook looks to be your best option. Indeed, at less than £300 per person, those prices seem to be real bargains. (I've searched for Christmas flights to the Canary Islands before, but later in the year, and found nothing less than £1000 per person).
Chris