A one day off peak travelcard from Gatwick to zones 1-6 costs exactly £10 - not 'about £11'. It's one ticket and you can buy it on the day at Gatwick. Use any non Gatwick Express train (after about 0930 in the week, any train at the weekend) to London, use the tubes and buses in London and then out to Heathrow.
Pro tip
Lonely Planet
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