Raised Bed Gardening
I have a similar problem in the Kitchen Garden. Our garden is surrounded by a yew hedge and this likes to send its roots into the raised beds. This year, following disappointing growth, I dug out the beds to find them choked with roots. I dug out as much of the root as possible and then added a lot of compost to the soil.
Adding a liner to your beds will make it harder for the roots to enter the beds, but won’t hold them off indefinitely. I now dig each raised bed over every time I am replacing the crops within it. This will keep the soil nice and loose and prevent the roots taking such a big hold again.
I hope this is useful for you. Please let me now if I can be of any further assistance.