Here's some more detail on your specific trip.
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This is how the following itinerary prices:-
27MAR JER-LGW BA2777 1930-2020
28MAR LHR-DFW BA193 1045-1540
01OCT DFW-LHR BA192 1835-0935+1
02OCT LGW-JER BA2776 1550-1650
Fare £148 + £128 (fare bases OLWUKJB and OLXUKJB)
Taxes fees and charges
USDA APHIS Fee (XA) £3.00
US Immigration Fee (XY) £4.20
US Customs Fee (YC) £3.30
United Kingdom Air Passengers Duty (GB) £13.00
BA YQ surcharge (YQ) £239.00
US International Arrival Tax (US) £10.40
United Kingdom Passenger Service Charge (UB) £29.82
United Kingdom Passenger Service Charge (UB) £15.11
United Kingdom Passenger Service Charge (UB) £7.06
US International Departure Tax (US) £10.40
US September 11th Security Fee (AY) £1.50
US Passenger Facility Charge (XF) £2.70
Total TFC £339.49
Total payable £615.49
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However, this is how the following following itinerary prices:-
27MAR JER-LGW
BA2771 0920-1010
28MAR LHR-DFW BA193 1045-1540
01OCT DFW-LHR BA192 1835-0935+1
02OCT LGW-JER BA2776 1550-1650
Fare
£300 + £128 (fare bases
NLWUKJB and OLXUKJB)
USDA APHIS Fee (XA) £3.00
US Immigration Fee (XY) £4.20
US Customs Fee (YC) £3.30
United Kingdom Air Passengers Duty (GB) £80.00
BA YQ surcharge (YQ) £239.00
US International Arrival Tax (US) £10.40
United Kingdom Passenger Service Charge (UB) £39.75
United Kingdom Passenger Service Charge (UB) £15.11
United Kingdom Passenger Service Charge (UB) £7.06
US International Departure Tax (US) £10.40
US September 11th Security Fee (AY) £1.50
US Passenger Facility Charge (XF) £2.70
Total TFC
£416.42
Total payable
£844.42
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The bolded items are those that are different because the second itinerary has a stopover (ie a stop of more than 24 hours).
The reason why fare OLWUKJB can't be used on the outbound half in the second itinerary is because of this fare rule in OLWUKJB:-
Stopover restrictions
STOPOVERS NOT PERMITTED ON THE FARE COMPONENT.
In contrast, fare NLWUKJB has this rule, and is therefore useable:-
Stopover restrictions
1 STOPOVER PERMITTED IN EACH DIRECTION AT GBP 150.00 EACH.
And the £150 charge has been built into the £300 you see as the "fare" above.
As before, there may be small variations between the exact figures quoted by this source and those quoted by BA, but these should be good enough to explain the difference in fares that you were seeing.
Keep the stop to less than 24 hours, and you will get access to the cheaper fares.