Nope. They only provide limos in the places where THEY operate to the final destination.
In this case, you're a transfer passenger, London isn't your final destination
You can play them at the "cheaper Ex-EU" game, but I wouldn't push it too far. To be clear, VS have investigated/audited FC members who have done the "AMS trick" - and indeed BA have - and in some cases (certainly in BA's case) they've cancelled freq. flyer accounts and removed all miles because of so-called "abuse". So, I'd say you can save the money by keeping it under the radar, but push your luck/point on the CDC transfer and you might lose more than a taxi ride...
As always, you may get lucky, but I genuinely wouldn't push the issue.
In this case, you're a transfer passenger, London isn't your final destination

You can play them at the "cheaper Ex-EU" game, but I wouldn't push it too far. To be clear, VS have investigated/audited FC members who have done the "AMS trick" - and indeed BA have - and in some cases (certainly in BA's case) they've cancelled freq. flyer accounts and removed all miles because of so-called "abuse". So, I'd say you can save the money by keeping it under the radar, but push your luck/point on the CDC transfer and you might lose more than a taxi ride...
As always, you may get lucky, but I genuinely wouldn't push the issue.