The Humberside Airport website states that the summer schedule applies to the end of October. The only flights listed as operating to Tenerife are charter services operating on Tuesdays and Fridays:
http://www.humbersideairport.com/huyweb.nsf/Co ntent/TenerifeSummer
The Tuesday service is flown by aircraft from Air Europa, under charter to First Choice. I've just tried some sample dates (out on 07/10, back on 21/10) and I was offered a fare of �228.56:
http://www.firstchoice.co.uk/
I can't track down any Friday flights. It's possible that they might not operate throughout the whole of the summer schedule or that the charter operators only sell the flights as part of a package deal (which is what applies to the majority of charter flights).
If you're prepared to consider alternative airports, Thomsonfly operate from Doncaster to Tenerife on Tuesdays and Fridays in October. The fare quoted (for the same dates as above) was �152.22.They also have a Friday service from Leeds-Bradford. (Out on 10/10, back on 24/10 is quoted at �199.98):
http://www.thomsonfly.com
However, the cheapest fares are likely to be with Jet2's scheduled service from Leeds-Bradford. The fare shown (for the same dates as above) was �139.18:
http://www.jet2.com/
Chris