EU No Frills Airlines you may not be aware of!

S7 backers behind the Cyprus airlines re-launch.

Vueling, part of the IAG group and sister airline to British Airways, based in Spain, but flying much Vueling.com
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Volotea, based in Palma Majorca, they fly from Southampton to Palma and Ibiza Volotea.com

Helvetic based in Zurich, they fly to Shannon , but also many other EU destinations ex Zurich
www.helvetic.com/

Norwegian, probably well known now, but they have a sizeable fleet ex Gatwick and fly as far a field as South America, North America and Thailand as well as many European Destinations www.norwegian.com

BlueAir a Romanian  carrier who fly from Glasgow, Liverpool, Birmingham and Luton to Romania destinations as well as direct to Cyprus from Luton  Blueairweb.com

Cobalt Airlines from Stansted, Birmingham, Manchester and Dublin to Larnaca  http://cobalt.aero/  as well as onward to Iran

Cyprus Airways relaunched by Russian airline backers (S7 airlines) using Charlie Airlines (Huge fleet), they don't currently fly to the UK, but watch this space https://www.cyprusairways.com/

AirEuropa  Madrid and palma carrier flying scheduled flights via the Madrid base to destinations over Spain   https://www.aireuropa.com/en/flights  Also they have a partnership with FlyLolo.com  flying flights to the Canary islands at Christmas   Gatwick, Manchester and Glasgow to Tenerife and Manchester to Arrecife (Lanzarote)  www.flylolo.com  

Best place to get an overview of all airlines including Easyjet.com and Ryanair.com is via Skyscanner.net the best search airgine for fares