In general yes, although there are ways to get round the issue. The new box should sit under the new TV & you could use Powerline adapters or Wi-fi to get the signal from the internet connection to the BT box.
https://www.shop.bt.com/category/net...homeplug/11301
https://www.amazon.co.uk/powerline-a...line%20adapter
Note that the performance of the Powerline adapters can be variable depending on your mains wiring so if you can you might like to find/borrow a pair you can test before buying a set. Whether Wi-fi is good enough depends on the proximity of your VDSL router & teh BT box.