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Make the stock. Put the lamb bones in a large heavy-based saucepan with the carrot, onion, celery, herbs, peppercorns and 1 tsp salt. Pour in 3 litres/5 ¼ pints water. Bring to the boil and simmer uncovered for 2 hours.
Strain the stock through a fine sieve to remove bones and vegetables, then return to the pan. Boil until reduced to about 1.3 litres/2 ¼ pints. (You can make the stock the day before – keep it in a covered container in the fridge, or freeze it for up to 3 months.)
Make the stew. Cut the lamb into large chunks. Peel the potatoes (keeping both types separate) and cut into pieces of similar size to the meat. Put the two different types in separate bowls of water to keep them white. Peel the carrots and cut into slightly smaller pieces. Slice the onions into thick rings.
Put the lamb in a large, clean saucepan. Pour in the stock and bring to the boil, skimming off all the impurities from the surface. Reduce the heat, cover and simmer gently for 10 minutes.
Add the floury potatoes, carrots and onions. Season generously and simmer for a further 10 minutes, stirring occasionally.
Add the waxy potatoes and thyme. Simmer until the lamb is tender (15-20 minutes). Take off the heat, cover (don’t stir) and leave for 15 minutes. (You can make this up to 2 days ahead and keep in the fridge). Garnish and serve.