You can determine if the problem is excess headspace simply by holding the bolt handle forward while firing the gun. (Wear a glove if it stings a bit.) Wrap a clean sheet of paper around the action to see if that stops the gas escape.
I suspect, though, that thousands of rounds have eroded the chamber and the leade so that gas is coming back around the case. You can check the fired cases to see if they have carbon smudges on them. If so, you might be able to have the barrel set back and rechambered, but if the chamber area is bad, chances are the rest of the barrel is just plain worn out. For that, there is no real solution, other than a new barrel, which might be hard to come by.
Maybe it is time to retire that old timer and look for a better .22, new or used.
Jim