A company has mistakenly deposited close to £2000 on my credit card. Can they take the money back out of my account? If not, how long before the money becomes mine legally?

I would be honest and report it to them, could be destined for someone really needing it.

Since this is their error, reported it you the credit card company, ask them for a letter of apology for their mistake, and some form of reward for your time and engery in correcting their error. Nothing is free anymore, it you made the error they would bill you.

They WILL find it and they WILL correct it. The money will never be legally yours. So report it to them ASAP.