LONDON—NatWest has been fined 265 million pounds ($350.9 million) for failing to prevent the laundering of nearly 400 million pounds, capping the first criminal money laundering case against a British bank. The fine would have been north of 300 million pounds, but a deduction was made for the bank’s guilty plea, the judge said. A criminal gang deposited hundreds of millions of pounds in cash at around 50 branches of NatWest, prosecutors for Britain’s financial regulator said on Monday, with at least one individual outlet receiving more than 40 million pounds. Couriers walked through the streets of British towns carrying bags of cash they then deposited at the bank’s branches before the scheme was busted by police, the Financial Conduct Authority (FCA) told the judge. One person in Walsall arrived at a branch with so much cash in bin liners—700,000 pounds0151—that they broke and the money had to be repacked …