Not sure, but I visited Pizza Express on both of my recent long DIYs, and I had to scan a QR code on a giant poster at the door which took me to their website, where I had to provide contact details before I was allowed into the restaurant.
Then, there was no physical menu, I had to select from the on-line menu.
The waiting staff took my order in person.
The poster said I had to pay on-line ( card and paypal offered ), not sure if they would have accepted contactless instead.
So I'd say that without a smartphone, you might well be out of luck.
Perhaps they offer some manual back-up option if you don't have a smartphone, dunno.