How do I kill the running app when I can't swipe upwards

I launched an app on my iPhone, and shortly after launch it stopped doing anything; but whatever it did has stopped the swipe-up gesture from working, so I can't get to the application switcher to kill it. I can use the side button to lock and unlock the phone, so I can get to the Lock Screen, and I can swipe down to get to the control centre, but no matter where or how much I swipe upwards the app just keeps running in the foreground. I don't think the app has hung, because I'd have thought the OS would have killed it by now; it just sits there intercepting the swipes. I have other things running in the background which I want to keep running, so I don't want to turn my phone off. I've seen that there are accessibility settings which might help... but they're no good to me as I can't get to the settings app. How do I kill the running app, without turning the phone off or changing any settings, when swiping up doesn't bring up the application switcher?