If you voted Independent and on that Independent platform that candidate won office would you expect them to function and behave as an Independent Councillor?
What if a year into office that candidate became a member of a party that you voted against in the election? What if a year into office they now believe in the principles and values of the party you oppose. Would you feel cheated?
What if their campaign and work in office is so closely aligned with those of the party you oppose, that the term 'Independent' becomes meaningless?
Can they still claim to be an Independent Councillor if in practice and principle they wholeheartedly believe in a political party?
At constituency level - wouldn't a MP doing the same trigger a bye-election?
Most Independent Councillors emphasize that they have no political affiliation - They seem to grasp the meaning of 'Independence'.
So why do some councillors blatantly disregard those who elected them on and Independent platform in the first place?
Would you be angry?
And should they make their change of allegience public?
Why keep the electorate in the dark?

Please
That says it all. Suppose I were to join the Conservative party and, having remained a member for a period of time, then announced that I wouldn't be renewing my membership for the coming year, would no longer pay my membership dues, and would feel free to ignore any of the rules and obligations of membership with which I was unhappy.
However I would still want to retain certain of the perks and privileges of membership which I'd enjoyed as a member in good standing, and the party ought to grant me what I ask because I'm a person of influence and significance in the community and in consequence they need my friendship and support, perhaps rather more than I need them.
I don't think they'd take my request seriously. Or me. And I suspect Mrs May and her team, assuming they're re-elected next Thursday, will experience a similar response when they begin to put their proposals to their erstwhile partners later in the month.
The "Rule Britannia" fallacy dies hard in the psyche of middle England and in the psyche of middle England's politicians. But what might have been realistic and possible in 1855 simply isn't realistic and possible now. And pretending and wishing won't make it so.