Charter airlines aren't always cheaper than scheduled flights. Budget airlines frequently offer scheduled flights cheaper than charters.
Since I know that you're near to Epping, I won't bother with flights from, say, Liverpool. I'll just suggest departure points from near to you:
easyJet fly a scheduled service, to Tenerife South, out of Gatwick:
http://www.easyjet.com/en/book/index.asp
Monarch offer scheduled flights from Gatwick and (closer to you) Luton:
http://www.flymonarch.com/
Unfortunately, there are no scheduled flights to Tenerife from Stansted.
However, Thomsonfly offers a charter service from Stansted to Tenerife South. The flights are only on Tuesdays and Fridays on the winter schedule and on Fridays only during the summer:
http://www.thomsonfly.com/
Trying some random dates (in June) on the Thomas Cook site identified direct charter flights from Gatwick to Tenerife South with Teleticket (�149), Excel (�149) and Avro (�176, also listed with Cosmos at the same price). There were cheaper flights (from both Gatwick and Heathrow) into both Tenerife North and Tenerife South with Iberia but those flights weren't direct:
http://ww1.thomascook.com/content/flights/home page/flights-homepage.asp
Chris