Britain’s beleaguered prime minister, Keir Starmer, suffered a gut punch on Friday, as his deputy prime minister, Angela Rayner, resigned after admitting that she had failed to pay adequate taxes on the purchase of a seaside apartment. Ms. Rayner, a plain-spoken politician who is popular on the left wing of the Labour Party, stepped down after an independent ethics adviser concluded she had breached the code of conduct for cabinet ministers. She underpaid the tax as part of a complex transaction involving another house that she had owned with her former husband, but then only remedied the error after weeks of public scrutiny. “I accept that I did not meet the highest standards in relation to my property purchase,” Ms. Rayner said in a letter to Mr. Starmer. You have been a trusted colleague and a true friend for many years.”