To a certain extent you need to prove where all money comes from to comply with money laundering regulations.Obviously banks don't bother about small amounts now and again.
No set amount, it depends on the normal conduct of your account. A market trader paying in load of cash would need to deposit a very large amount before raising a query, but someone who just gets a regular salary/pension by BACS would get flagged up if they suddenly paid in large sum/sums
Your title says 'opening an account'. I think they may look more closely at a large payment into a new account than they would for a customer they know well.