Hi DebJ,
As my friends CL and Hevleigh have mentioned, flights into Larnaca are throughout the day (most Tour Operators fly Weds or Sun from the UK). There are scheduled flights every day of the week (from somewhere), although winter can be a little tricky getting to Larnaca, but I digress...
Now, Tour Operators often have exclusive arrangements with accommodation, meaning that they block-book the place for their customers.
What this means to you, perhaps, is that if you are stuck with using Airtours for your preferred accommodation; Airtours use MyTravel for their flights (same people)...
...then Mytravel fly to Larnaca from: Birmingham, Bristol, Cardiff, Durham Tees Valley, Gatwick, Humberside, Leeds/Bradford, Manchester, Newcastle, East Midlands and Stansted.
Sorry for the long post, but I hope this helps in your search.
Ady