Before retirement one of my tasks was training ML ATC for the INTAS. As such I came into contact with just about every other part of the new tower project and I queried the fate of the old tower.
The old tower does have heritage value but this doesn't mean that it has to be preserved. Some artefacts Will be and there are also photographic records.
The new tower was built using a slip ring which moved up as concrete was poured. The new tower will probably be demolished in reverse. I.e. A ring will move down and carry the rubble.
As DB said, the old tower has concrete cancer. It was never painted when constructed thereby allowing the concrete to absorb atmospheric carbon dioxide which eventually reaches the steel rods causing the cancer. The cancer was treated in the mid 90s and the tower painted.
To prevent cancer in the new tower, the builders used the same technique used on road bridges and painted it.