Put the trotters in a pan and cover with water. Bring to the boil, cover and simmer for 1 hour, skimming off any scum that rises to the surface. Reserve the liquid and trotters.
Melt the butter and oil in a flameproof casserole dish. Quickly brown the pigeons, then remove and reserve. Add the onions, carrot, celery and bacon to the pan with the cinnamon, bay leaf and thyme. Stir to coat with the fat, then reduce the heat, cover and sweat gently for 10 minutes. Sprinkle with the flour and stir.
Return the pigeons to the pan, together with the trotters, prunes, parsley, wine and 600ml/1pt of the reserved cooking liquid. Season lightly with salt and pepper. Bring to the boil, cover and simmer gently, turning the pigeons occasionally, for 45–60 minutes, until tender. Serve hot.