Yes, at most banks. The offers ask you to pay money in, and a transfer from another account in your name counts. Barclays is the exception. It wants a salary, a pension or a transfer from a UK business account.
What you do need is the pay-in amount to move, which is £1,000 to £2,000, and the direct debits the offer asks for.
The one that needs a salary
Barclays wants "a salary of at least £2,000" paid into the new account within 30 days of opening it, and again each month for the extra £30 payments. A transfer from your own savings won’t meet that. A pension, or a transfer from a UK business account such as a sole trader’s, does. If you’re about to start a job,
the first salary guide covers timing it.
The same £1,000 to £2,000 can be paid into one account, counted, and moved on to the next.