Can council make you get rid of a dog if it's private rented?

you would not be here if you did not think council could

Same question, same answer - (https://uk.answers.yahoo.com/question/index?qid=20161115044556AANhxJw)

"Well there's nothing like defusing a situation to say 'Woof' to somebody who is complaining about noise, and walking off!! Not.

However, if you are renting privately, with WRITTEN permission to have dogs in there, and most would stipulate how many to be honest, then you should be okay. But if this neighbour took this further, which she might, and involves your landlord, you may find yourself in hot water if your dog(s) are making a nuisance of themselves. I have to question how you know that your dogs settle down if you are not there? If this becomes an ongoing nuisance, your landlord may change her mind about allowing you to have dogs in there which could mean you have to find alternative accommodation, and that property becoming out of bounds to anybody else with dogs, needing to rent. As landlords who will allow dogs in their properties are becoming fewer and fewer, that would be tragic as far as I'm concerned.

When you rent, you are not right in saying 'no one can make me get rid of them'. Again if your dog(s) are a nuisance, the landlord certainly can even if 'the Council' can't. And even if you own a property, if your dogs made lots of noise and disturbed neighbours in hearing distance, the Council could require you to control the noise your dogs make, and if you don't ask you to get rid of them. "

If its a noise nuisance or aggressive, or a banned breed, then yes they can.
If not then see a solicitor. If you cant afford one, google for your local Law Centre, or talk to Cooper and Co;

http://doglaw.co.uk