The phone quote does seem to be on the higher side. Also, on your way back, consider flying via AY (Finnair). You will likely have only a short connection in HEL, and might be able to get 4 saver seats in J. Also, the taxes will be lower than if flying on BA (although not too different). The one caveat is that your dates are for peak travel to India.

The flight is pretty well timed - leaves DEL at around 10:40 am and arrives into LHR at 17:00, with a two hour layover in HEL.

QR is also an option but with crazy departure times from DEL and longer layovers in DOH, is not quite suitable.

To see all this availability, you will need to create an account on BA, and search for award redemption using Avios miles - it will show you how many saver award seats are available for each itinerary. Then you can call AA and give them the exact flight #s. Usually it works well.

EK is a hit and miss. I have never been lucky finding any availability. And you will likely run into the same issue as QR - not so ideal timing.


EDIT: for 4 Jan, I see 5 Off-peak seats available in J (30k AA miles each).
10:40 DEL 14:45 4 Jan HEL Finnair - AY0022
16:55 HEL 18:10 4 Jan LHR British Airways - BA0799
OFF-PEAK