An EU regulation was passed in Brussels last month which means from October all providers of cashback credit cards will be in the same position.
Thanks.
On the American Express point I note the article says:
"The price cap will not apply to so-called three-party card schemes, such as Diners and American Express, which involve only one bank. Commercial cards used only for business expenses will also be exempt from the new price cap."
Therefore looks like American Express is the best option (presuming they are still doing their cashback deal).