Britain’s deputy prime minister, Angela Rayner, acknowledged on Wednesday that she had failed to pay adequate taxes when she bought a seaside apartment, raising questions about whether she can hold on to her position and creating another political headache for Prime Minister Keir Starmer. Ms. Rayner said she had not tried to evade taxes, having relied on legal advice about how to handle a complex property transaction that involved another house she owned with her ex-husband. For Mr. Starmer, whose government has struggled to find political traction amid a stagnant economy and erratic economic policies, Ms. Rayner’s admission is a major new distraction. Adding to the political complications for Mr. Starmer, Ms. Rayner is the government’s top housing minister. She is spearheading a Labour pledge to build 1.5 million additional homes in the five-year term of this Parliament.