American Express offers in other markets are irrelevant. What UK-issued cards offer no foreign transaction fees -and- compelling rewards?
When MBNA/EK decided to withdraw the AMEX/VISA cards from the UK market they sent me the MBNA VISA horizon card.
No annual fee
0.5% cashback on spend even overseas (this more than covers the 0.3% interchange fees for overseas transactions)
No forex fees.
In fact I have left it as my default card for UBER and have used it in 8 countries and the exchange rate is brilliant.
The only problem is that I do not know whether they have started offering it to new customers yet.