LONDON—BP PLC shares rose to levels not seen since shortly after the Deepwater Horizon disaster in 2010, as rebounding oil prices led to solid first-quarter results.
Like other big oil firms that have reported recently, London-based BP benefited from recently lofty oil prices, but it also showed rising production. The outcome was its strongest quarterly earnings since mid-2014—which could go some way toward convincing investors that BP’s ambitious plan to regain its position among the world’s top energy companies is gaining...