To continue the story I started in the post below .... I noticed that the foreign exchange at Marks and Spencers also did a very good rate - in fact, over the counter, within two tenths of a cent of the same rate that I could get online at the post office. So I went there.
They didn't charge commission. However ... they said that if I withdrew money using a Barclays debit card (debit card!!) then Barclays would charge commission. I have to say that this baffled me - since when have a bank charged for using a debit card for making a cash withdrawal?!
However, I went to a cashpoint, withdrew (free) £300, went back to Marks and Spencers, and exchanged it for dollars.
Had I bought dollars at the airport, £300 would have bought me around $425. A week or so later, at Marks and Spencers, about £299 bought me $455. The exchange rate had changed in that time, and this accounts for around half the difference.
It's also worth noting that if you order money in advance to collect from the airport, the exchange rates are far less punitive.