Some years ago, when I was in business, I asked my bank about the safety or otherwise of giving out my bank account number and sort code. The bank assured me it was safe and standard practice. Knowing this information will allow anyone to pay money IN to the account but does not allow anyone to take money OUT. I assume this is still true but please correct me if I'm wrong.
Although that is correct, and years ago it probably didn't matter, its best to be cautions these days.
Jeremy Clarkson once gave the world his bank account and sort code to prove this point, and someone set up a direct debit to a charity in his name and it paid out.
Important to be aware that phishing scammers gather as much information as they can before launching a sophisticated con pretending to be the police or the bank etc etc. 99% of the time you are on your guard and spot them coming, but that 1% is when by co-incidence you were expecting their call and the information they have about you they use to allay concerns.
My elderly mother got called by the police in London to say they had caught a fraudster trying to pass off my fathers credit card. They new the sort code, bank account number etc its all seemed plausible to start with, she had a 30 minute call going into the details of what was supposedly being fraudulently purchased, then they asked a question about a bank detail that raised suspicions and luckily she was NOT in a rush, had her wits about her, and so she put the phone down and phoned the local bank branch to find out it was a fraud. If she had been in a rush she would probably done what she was asked to do, but luckily she was at home feeling calm.
At work last week, we received an invoice from a new supplier, one we had recently contacted with, the email was 'supposedly from the supplier' it had our bank account etc and theirs, it just needed goods inwards to electronically tick the sign button, as you do these days. Luckily they checked with accounts etc. Turned out its was a sophisticated scam from North Korea, we won a vaccine contract from the government earlier this year and appears the publicity had attracted the attention of Chinese, Russian and N Korean hit list for sophisticated phishing. Trying to get the science information and our money.
So my advice is give as little away as you have to.