Thinking this through I can't any British citizen being willing to fight in a war whatever the circumstances, including where the UK was being invaded by a brutal authoritarian regime.
Looking at this logically, the citizens most likely to feel the patriotic need to join up, defend the country and do the actual fighting and dying would be young white men of all classes, that are often perceived as right wing.
Those least likely to be willing to join up, fight and potentially die would include the progressives, those perceived as left wing, the woke, the old and of course women.
Now under an authoritarian regime the group most likely to get imprisoned or have their rights curtailed, or persecuted and potentially executed or get thrown off tall buildings is definitely not young white males of all classes.
So this creates the key question of why would right leaning young white males of all classes want to join up, fight and potentially die to protect the rights and lives of the section of society that despises or blames them when they are the section of society least at risk.
To paraphrase Niemoller:
First they came for the protesters and left wing
And they did nothing until it was too late
Because they thought someone else should do it for them.
Then came for the progressives and woke.
And they did nothing until it was too late
Because they thought someone else should do it for them.
Then they restricted the rights and privileges of the old and women
And they did nothing until it was too late
Because they thought someone else should do it for them
Then they left me alone
Because they knew that I would fight them if they did and even if they did and won then that would mean that there would be no one left and they would have an empty country.
In summary those most likely to suffer from the UK being attacked and run by a foreign authoritarian regime are the ones least likely to be willing to join up, fight and potentially die for their rights, freedoms and in the extreme their lives, whilst expecting those that are least likely to suffer to join up, fight and potentially die for their rights and freedoms and lives.