You need to understand the big difference between websites which try to find you the cheapest hotel prices (such as Trivago) and those which claim to get you the best airfares (such as SkyScanner):
Most hoteliers are happy for their accommodation to appear on sites such as Trivago, as that brings their hotels to a much wider audience than simply having their own websites online.
However many airlines (particularly budget carriers) totally DETEST 'screenscraper' websites, such as SkyScanner, and do their very best to ensure that their own fares DON'T appear on such sites. (Some budget airlines even refuse to honour bookings made through 'screenscrapers'). That's because budget airlines make most of their money through selling 'extras' (such as upgrades, accommodation and car hire), rather than through the cost of their tickets. So it's important to them that passengers book through the airlines' OWN websites, where they can be offered all of those 'extras', rather than through any third-party site.
So, despite the claims of SkyScanner (et al) that they'll always find you the best fares, they often CAN'T because they're unaware of the real bargains.
So the best way to carry out a search for the lowest fares is to do it yourself (i.e. without the aid of any 'fare finder' websites). I've helped loads of AB members find cheap fares in the past. I'd be happy to try to do the same for you but, if you'd prefer to have a go yourself, here's my technique:
Step 1: Open the Wikipedia pages of both the relevant UK airport(s) and the destination airport(s). Check to see if there are any direct flights available. If there are, go to the websites of the relevant airlines and check their fares ;
Step 2: If there are no direct flights, or you're prepared to consider using connecting flights to save money, look through the Wikipedia pages to find potential connecting airports that are served from both UK airport(s) and the destination airports. Then check on fare and connections on the websites of the airlines involved.
Things to remember:
1. There may be alternative airports available that you don't immediately think of. For example, if you're going to Barcelona you're not restricted to using just Barcelona's (wonderfully named) El Prat Airport. Both Reus and Girona Airports are nearby, with direct buses running into Barcelona.
2. You don't have to use the same airline(s) in both directions.
3. You don't need to use the same airports in both directions. (For example, if you're getting to your UK airport on public transport, so that you don't have to park your car, you can fly out from Stansted but fly back into Gatwick).
4. Some airlines are heavily subsidised by their national governments. In particular, China provides massive subsidies to Air China, China Eastern and China Southern so they can offer really cheap fares. Therefore for any long-haul flights which might be possible to route via China, it's well worth looking into taking that route.
If you need help searching, just ask here. I love beating SkyScanner ;-)