I have a connection in Heathrow to Switzerland, but was interesting in obtaining euros for subsequent travel beyond Switzerland which uses CH. Does Heathrow have ATMs which dispense euros?
It appears that Travelex has a "click-and-collect" service at Heathrow. Travelex operates a lot of the expensive ATMs you see in airports. I wouldn't use the service, because I'm sure the exchange rate is quite poor. I suspect it would be cheaper to get a small quantity of euros from your bank or other source before you leave home if you're really uncomfortable waiting until you arrive in your first euro country. These days, credit cards are so readily usable that I wouldn't feel uncomfortable without cash until I came across an ATM somewhere in my first euro city.
There will likely be two conversion fees.
First, if your bank card is in US dollars that will be used to buy Sterling from the UK ATM, and then those pounds will be used to buy euros. This will happen behind the scenes - you won't get pound notes but the transaction will appear on your bank statement later. So unless you are buying euros with pounds this isn't a great idea.
Just hit an ATM as soon as you enter the EUR zone.
I was at the Travelex desk in MAN yesterday. I was collecting €100 for my trip to Mallorca, ordered online a few days earlier. I got a rate of 1.11 to the £ on Saturday. If I had just bought them yesterday at the desk they would have been 0.91 to the £. I would imagine that the multi currency ATMs (MAN has £\€\US$ machines) have equally bad exchange rates on the day.