You can often find the cheapest flights by going direct to the websites of the relevant airlines.
The Robin Hood airport flight schedule
http://www.robinhoodairport.com/show_image.php ?file_id=376
shows that the following budget airlines operate from there:
Thomsonfly (to Amsterdam, Alicante, Faro, Geneva, Ibiza, Malage, Palma de Mallorca, Prague & Pisa):
http://www.thomsonfly.com/en/index.html
Ryanair (to Girona/Barcelona, Dublin & Pisa):
http://www.ryanair.com/site/EN/
FlyBe (to Belfast):
http://www.flybe.com/
Wizz Air (to Gdansk & Katowice/Cracow):
http://wizzair.com/default.asp
FlyGlobeSpan (to Toronto):
http://www.flyglobespan.com/index.asp?lan=en
Some of the charter operators from Robin Hood (listed in the first link, above) might also offer flight-only deals. Check the relevant websites.
Here's a list of the (summer) destinations served from East Midlands. Click on the destinations which interest you, to see who flies there. In each case, you'll find a link to the relevant operator. (The principal scheduled operator from East Midlands is Ryanair):
http://www.eastmidlandsairport.com/cms/9/summe r-destinations.html
Chris