Put the chicken stock in a casserole dish large enough to hold the chicken, together with the herbs, sliced carrot, onion, salt and cayenne pepper.
Bring to the boil and lower the chicken into the stock.
Allow to poach at a gentle simmer for 20 minutes.
Put in the lemon rind (thinly pared) and the juice of the lemon and simmer for a further 20-25 minutes.
Lift out the chicken, tipping it to drain off the liquid inside, and keep it hot.
Strain the broth into a measuring jug.
In a smaller pan, melt 1½ oz.
of the butter and stir in the flour.
Stir over a gentle heat until it sizzles.
Add 20 oz. of the chicken broth, a little at a time, stirring between each addition.
Simmer the resulting sauce for 15 minutes, stirring occasionally, taste for seasoning and add the mushrooms, sliced and sautéed gently in the remaining butter for a few minutes until they are just tender.
Lastly, stir in the cream and pour the sauce over the chicken.