There are two ways in which the stopover rule will increase the fare....a stopover is generally defined as a stay over 24 hours:

1 - with a stopover on an exUK-UK-exUK itinerary you have to pay UK Air Passenger Duty. If just transiting the UK (no stopover) you don't. APD is expensive and looking at the OP is probably the reason for the fare difference here.

2 - Some fares allow a stopover for free. Sometimes the cheapest fare on a route won't allow a stopover at all. The next more expensive fares may charge a fee. The most expensive will typically not charge a fee or the fee will be lower. This varies hugely by route and cabin flown.