British Airways — the largest airline in the United Kingdom — is notorious for charging large fuel surcharges for their flights across the Atlantic and offering scanty awards seats on their own flights. (creditcards.com)
Alitalia charges large fuel surcharges on its own flights and partner airline flights, but, if you do some searching, you can find good values despite the surcharges and you can sometimes get a lower fuel surcharge by booking a partner airline through Alitalia than directly with that airline. (creditcards.com)
Avios are a decent way to upgrade to business class though, for transcon flights, if you don't mind large fuel surcharges. (doctorofcredit.com)