Heat vegetable oil on medium-high heat in alarge soup pot and brown all the meats. Do not move the meat while browning, get it seared on each side and then put in a bowl. Sauté onions, carrots, celery and put in the pot and brown them. If necessary, add more oil to the pot. Sprinkle salt over the vegetables. When the vegetables are well browned, add the garlic and cook for 30 seconds more, until you can really smell it.
Return the meats to the pot and the chicken and beef broths and the tomatoes and stir. Bring to a simmer, cover, reduce the heat and simmer gently for 2 hours. Remove the meat pieces, strip from bones and cut into smaller pieces, return to pot.
Uncover and remove the meat pieces. Strip the chicken off the bone and discard skin if you want. Return all the meat pieces to the pot and bring it up to a strong simmer.Add potatoesPeel and cut the potatoes into chunks about the same size as the meat . Add them to the stew and cook them until they are done, about 45 minutes. When the potatoes are done, add the Worcestershire sauce, mix well and taste for salt.
Add more Worcestershire sauce to taste if needed. Add the corn and peas.Mix well and cook for at least 10 minutes,but no harm in letting it simmer longer.