Thanks for the info.
easyJet, Monarch, Thomson and Thomas Cook are quite a bit more expensive (but see below re Thomson).
Ryanair is around £109, so it might be worth considering whether the final price (i.e. with baggage charges, etc) is much different to that offered by Jet2 (and, of course, seeing which airline has the most convenient flight times for you). It could also be worth looking at whether it makes most sense to travel out with one airline and back with another.
I've checked the websites of both airports (and Wikipedia). They all confirm that the five airlines I've checked (plus Jet2) are the only ones flying from Manchester to Tenerife South.
So it looks like it's a choice between Jet2, Ryanair or, just possibly, Thomson - They offer £129 on a charter flight out on 22/05 and back on 29/05 - If they've got fewer 'extras' than, say, Ryanair, they might not actually be any more expensive in total.
Chris