Well, not as save as your money is in a U.S. bank, but I doubt any banks here will fail, so pretty safe.
In the U.S. you get 100% protection up to $100,000 and up to 250,000 for some retirement investments.
In the UK the first £2,000 is covered 100% then you are covered up to 35,000 by 90%.
I suppose removing all your money would depend on the bank and your account.