I think the question should be “why are you carrying about that amount of cash anyway?” I don’t think your arguments about cost stack up, you can get a good hotel in London for far less half the amount you mention and a meal for two for far less than £100. The only thing I would agree with you is the cab rate to/from Central London to LHR and you might have underestimated at certain times.
In these days of credit cards there is no need to carry that amount of cash. Hotel bills, meals can all be paid for without cash. The reason why people are stopped and checked is because of money laundering, look at what you are carrying.
In answer to your question, I suspect you are the exception, personally I only take about £100 worth of local currency if that, there are holes in the wall to get cash.