You do realise that it isn’t Theresa May that arranges your refuge collection. Of course, you do, only joking.
Local government is very different to national government. For a start, local councillors do not get paid, other than legitimate expenses. Also they do not set your council tax for the most part - that is set at county level. And show me a county council of any colour that does not increase its council tax each year?
For the most part, although the councillors do have a party affiliation, what they do is nothing to do with the party. They use their skills and experience to utilise the budgets they are given to the best of their ability. Where councils have had a smallish change, I doubt you’ll see any difference even where they have changed overall control. But they will miss the expertise and experience that is lost, and where councils are mostly fresh faces their will be a severe drop in knowledge and ability that will take some months/years to re-establish.
Imagine your team at work. Say an experienced guy left and was replaced with a new guy with no previous experience. You would probably manage and be able to bring them up to speed. Now imagine that all or most of your team are replaced with new guys with no previous experience. I imagine you would see a drop in capability of your team that would take some time to build back up.
Cheers,
Nigel