Chests of drawers
Good quality furniture can be donated to local charities using the reuse container at some local Household Recycling Centres. They may be suitable for reuse through a local reuse network such as Freecycle or Freegle. There are now a large number of reuse groups on Facebook.
Alternatively, some charities might collect these items from your home. Chests of drawers which are unsuitable for reuse can be included in the wood or metal skips at your local Household Recycling Centre, depending on what the furniture is made from.