A huge number of UK package holiday prices are based on flights from London Gatwick, with various supplements if you wish to fly from other airports around the country. Being flexible about your departure airport could save you money, but obviously you need to offset this against the cost of getting there, be that train fare or petrol and parking costs. If you're travelling last minute, you can often find amazing deals if you look at different airports (the big ones book up fast!) so take the time to work out if you have any options beyond the obvious.
When it comes to longer journeys, adding a connection can reduce cost or it may even be a requirement for a long-haul trip. A connection could give you a change to explore somewhere new, since a lot of airlines will let you stopover for a day or two without it affecting the cost of the combined flights. Fly to New York via Reykjavik, explore Chicago on your way to LA, stop off in Dubai on your way to China or Thailand, hit up Hong Kong or Singapore before heading to Australia, or have a few days in Fiji on your way to New Zealand.