No that isn't true. About 23% of council funding comes from central government, the rest is raised locally or comes out of reserves, and a proportion of the business rates they must send back to central government www.instituteforgovernment.org.uk/explainers/local-government-funding-england
Perhaps you haven't noticed how many councils are on or over the brink of bankruptcy?
As somebody else has commented, some 60%+ is spent on social care alone (in my council it is 68% this year). Council tax isn't a buffet menu - no more than income tax or VAT - you don't get to opt out by "cutting back". Personally I don't use the armed services and don't want to, but nobody is giving me my income tax back. I haven't used schools in the UK for 42 years - nobody is giving me a refund on that either.
We all have bills to pay. We could all cry over that. It isn't just the OP, but it doesn't mean we get to bash the local council for putting up the central government mandated local taxation to pay for the things that we as a society use. FWIIW, as a council employee, my "payrise" this year and last year both resulted in a reduction of my take home pay, and my pay today is worth 25% less than my pay in 2010. At the same time we are doing three times more work with what is now approaching half the staff we had back then. That makes me cry too. Then council staff get bashed for being "well off" (we aren't), lazy, negligent etc etc. So forgive me if I am fed up to the back teeth of being told that everyone elses ability to pay their bills is more important than the ability of me and my collegaues to pay theirs and then being blamed for not having the resources to meet everyobodys demands day after day after day.
If I were not a few months from retirement I'd be out of public service like a shot (and actually could be - my skills are in demand in the private sector, but I have a social conscience and thought I should use them to help people). I used to love working with and for people - I specialise in supporting the most deprived, disadvantaged and vulnerable communities. But it just isn't worth it any more. We are routinely abused, criticised and bashed because it seems that it is our "overpaid" fault that there are no services left. Anyone who enters public service these days needs their head testing.