Funkyfifi

Hi, I really hope its OK to post this here and apologies if I don't include enough information. I've shown a photo of my beloved Holly tree and it's location. It's been growing here for years and I've recently moved back to my childhood home after losing my Mum. It was her favourite tree, so I'm very protective of it. My new neighbours have permitted development passed for a single storey kitchen extension which will replace the fence behind the tree..... Obviously they will have to dig a foundation of around a metre, and cut some roots. I'm not massively happy, but want them to be able to build what they want and not cause problems. Would a mature holly tree be likely to survive this in your opinion? There's about 6 inches between the trunk and fence if that helps? I have literally no idea if it's doomed or if there's anything I can do to help it? Thanks so much again xxxx