I tend to use SkyScanner to search for flights- it will let you choose where you fly from/ to (airport/ city/ country, etc) or you can specify where you want to fly from, and leave the destination empty to search for all flights from that location. I have found some pretty good deals through there- UK to various places in Europe for under £100 return, London to Bangkok for ~£400-£500 return, etc.
Edit
This is the sort of results page I get when searching for flights from London to Anywhere:
If I click on one of those options, it gives me a list of the available flights for that destination (in this case, cities within the country selected):
If I then select a flight (city) for that destination, it gives me a list of flight comparisons for different airlines: