Congrats on the mileage accumulation. Well done.
I've only been to Paris and London, never take more than a couple hundred of cash with me. Then use the ATM machines. They work like a charm.
Have fun.
I don't know how long your layover in LHR is, but if it's several hours, grab the train into Paddington station for a quick look around.
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TANSTAAFL - but if you work it right, FF miles comes pretty close.