This is very common on the autos, happens to mine too; it's the differential. It was the same on XJSs, which used the same one; it's not something to worry about.
So you're saying not to use first gear inhibit?Also advised not to use first in the auto as well.That is
why the warning on the dash when it is off.YOU DO NOT
NEED IT.Put in Sport instead.
+1, start here first and see how she goes as it could still be on its original drive train oil for all you know.The oil in the diff should be replaced every 30,000 miles. It is also advised to use an additive to prolong its life.
Wayne is correct, I used to have an old Granada that howled like a wolf and she never blew on me and I drove her to UK & Germany all the time over a 3 year period with no problems ( just the howl ) I changed the diff oil each year too and had NO leaks either from the seal.New oil may quieten it a little, how ever the crown wheel and pinion are probably getting worn.
Sometimes they are set up on the loose side at GKN Salisbury, so just a slight amount of wear is enough to make them "sing or howl".
I wouldn't worry about it too much, they can make noise and still last a hell of a long time.