The short answer is: Yes. It can cause problems with a possible MOT, because according to legislation, a TPMS system (for cars from 2018) may not indicate a defect. And the system in your car will indicate this because it does not receive any signal from the sensors. The sensors are still in the summer tires

To avoid problems, you can clone / copy the current ID numbers of your sensors to (empty) universal sensors. Because the car already recognizes the ID numbers, these do not have to be re-taught to the car. You can also use pre-programmed sensors, only then you have to re-teach the sensors to the car every time you change your tires.