I'll start by saying that the taxes and fees are higher if you fly into LHR, so that can offset any savings, or at least that's what happens to me. If you book with points you can book 2 one-way flights without any upcharge.
I agree that if you are paying cash it's not a good deal.
As to which airport, I honestly think it depends on where you are flying from. We used to fly into London, but lately there's been a great AF flight from here to Paris (nonstop) that is beating the prices of the flights into London, whether I pay by points or cash. We use AMEX MRs to book the Air France flights (and the British Air flights) that we are taking. Things change often, since this AF flight wasn't really on my radar until recently and now my family has booked 3 trips for 2018-2019 to other parts of Europe using that flight. Are you doing points or cash? I used awardhacker to find points based flights and Google flights just to see what was out there.
We've taken the chunnel train before and it was fun, convenient and easy (much easier than flying).
Are you trying to book with cash or points?
Total enablers. But I'm going to add to the "grab the CIP 2 while you can" group. 105K+ URs for one card is a pretty sweet deal. And it doesn't add to your number of accounts.