Not sure why using a smartphone wouldn't work, but yes you can use your debit or credit card to pay in almost every place in the UK now.
And most of them do (and prefer) contactless, for which your phone should work just fine, unless yours won't let you download any of the apps that can be used (there are a few, depending on whether it is iPhone or Android and which brand), due to your location.
This is the nub of the issue for me. Living in Germany, I honestly have no clue which apps you need on a smartphone in order to initiate smart payment and I seriously doubt I would be able to download them any way because of the fact my phone uses the German app store. I'm no longer eligible to have a British bank account and my German bank doesn't use contactless payment as far as I'm aware, so ultimately the use of a phone for contactless payment is closed to me for the time being. I just wonder about all of the overseas tourists coming to Britain and wether this is an issue or not.
Another thing that has occurred to me is the fact that I may well be charged for all of my transactions using a card and stung for the exchange rate. In the past it has always been cheaper and easier to withdraw a chunk of cash and just use that, with that avenue potentially closed and the smart phone avenue unavailable, visiting Britain could well have got a heck of a lot more expensive.
Please note the above paragraph is all complete conjecture and thinking aloud from me, I'm intrigued now to find out if the above is indeed the case.