All you're missing is the fact that FI doesn't have YQ charge on this route.
That's all. Check other airlines. It will show you YQ or YR.
Here's BA fare break down
How to buy this ticket
Tickets cannot be purchased directly from ITA Software.
Provide this information to a travel agent to help them match the fares found.
Make sure to provide the exact booking and fare codes shown.
Fare 1: Carrier BA OHW7Q3D1 WAS to LON (rules)
Passenger type ADT, round trip fare, booking code O
Covers IAD-LHR (Economy)
$294.50
Fare 2: Carrier BA OHW7Q3D1 LON to WAS (rules)
Passenger type ADT, round trip fare, booking code O
Covers LHR-IAD (Economy)
$294.50
(YQ) $458.00
US International Departure Tax (US) $17.20
US September 11th Security Fee (AY) $2.50
US Passenger Facility Charge (XF) $4.50
USDA APHIS Fee (XA) $5.00
US Immigration Fee (XY) $7.00
US Customs Fee (YC) $5.50
United Kingdom Air Passengers Duty (GB) $105.10
United Kingdom Passenger Service Charge (UB) $62.40
US International Arrival Tax (US) $17.20
Subtotal per passenger $1,273.40
Number of passengers x1
TOTAL AIRFARE & TAXES $1,273.40
This ticket is non-refundable.
Changes to this ticket will incur a penalty fee.
Fare construction (can be useful to travel agents)
WAS BA LON M 294.50OHW7Q3D1 BA WAS M 294.50OHW7Q3D1 NUC 589.00 END ROE 1.00 XT 5.50YC 7.00XY 5.00XA 34.40US 2.50AY 105.10GB 62.40UB 458.00YQ 4.50XF IAD4.50
Here's UA fare break down
How to buy this ticket
Tickets cannot be purchased directly from ITA Software.
Provide this information to a travel agent to help them match the fares found.
Make sure to provide the exact booking and fare codes shown.
Fare 1: Carrier UA LHWNC10S WAS to LON (rules)
Passenger type ADT, round trip fare, booking code L
Covers IAD-LHR (Economy)
$294.50
Fare 2: Carrier UA LHWNC10S LON to WAS (rules)
Passenger type ADT, round trip fare, booking code L
Covers LHR-IAD (Economy)
$294.50
UA YQ surcharge (YQ) $478.00
US International Departure Tax (US) $17.20
US September 11th Security Fee (AY) $2.50
US Passenger Facility Charge (XF) $4.50
USDA APHIS Fee (XA) $5.00
US Immigration Fee (XY) $7.00
US Customs Fee (YC) $5.50
United Kingdom Air Passengers Duty (GB) $105.10
United Kingdom Passenger Service Charge (UB) $54.10
US International Arrival Tax (US) $17.20
Subtotal per passenger $1,285.10
Number of passengers x1
TOTAL AIRFARE & TAXES $1,285.10
This ticket is non-refundable.
Changes to this ticket will incur a penalty fee.
Fare construction (can be useful to travel agents)
WAS UA LON 294.50LHWNC10S UA WAS 294.50LHWNC10S NUC 589.00 END ROE 1.00 XT 5.50YC 7.00XY 5.00XA 34.40US 2.50AY 105.10GB 54.10UB 478.00YQ 4.50XF IAD4.50