The rule of thumb is all extras levied on a commercial fare apply to the equivalent BAEC redemption fare.

So for example, LHR-DUB-JFK one way in theory works out at 25,000 BA Miles plus the following cash components (totalling £168.84)

£30.24 EI YQ surcharge (YQ)
£12.00 EI YR surcharge (YR)
£60.00 United Kingdom Air Passengers Duty (GB)
£21.80 United Kingdom Passenger Service Charge (UB)
£ 6.60 Irish Inspection/Pre-Clearance Charge (UQ)
£ 3.10 USDA APHIS Fee (XA)
£ 4.30 US Immigration Fee (XY)
£ 3.40 US Customs Fee (YC)
£14.80 Irish Passenger Charge (UP)
£ 2.60 Irish Air Travel Tax (LQ)
£10.00 US International Arrival Tax (US)

So, as you can see EI does levy a fuel surcharge for the TATL sector but at £30.24 it is lower than BA's (which together with BA's Insurance fee totals £87.50). There is an additional £12 fuel surcharge which applies to the short LHR-DUB sector.

So this represents a £30 saving compared to a direct one-way LHR-JFK on BA. If you can work in a min 24 hour stopover in Dublin, then the UK APD need not apply (saving £60.00)