It is obvious that the language of a statute must be understood in the sense in which it was understood when it was passed, and those who lived at or near the time when it was passed may reasonably be supposed to be better acquainted than their descendents with the cicumstances to which it had relation, as well as with the sense then attached to legislative expressions.
The fixation thesis was the source of the maxim contemporanea expositio est fortissima in lege. The contemporaneous exposition need not be legally binding. If Lord Coke thought a statute meant X, then that was evidence it meant X, even when legislative history could not be admitted for interpreting recent statutes.
The phrase "circumstances to which it had relation" might seem to indicate an "expected application" theory of meaning. However, the English courts only applied the contemporanea expositio principle to very old statutes (more than a century) for which it could reasonably be assumed that linguistic change in the semantics of words had taken place: Campbell College, Belfast v. Commissioner of Valuation for Northern Ireland,  1 W.L.R. 912 (H.L.) at p. 941. So the expected application of long ago was only relevant to the semantic/intensional meaning that could be inferred from it.
Interestingly, at a time when stare decisis was still considered absolute, it did not apply to mistaken statutory interpretations on constitutional grounds.