LONDON ( TheStreet) -- BP ( BP) said Friday the costs of responding to the oil spill in the Gulf of Mexico have reached $8 billion. BP, in a statement on its Web site, said it has made 127,000 claims payments totaling about $399 million. BP said the well has been shut since July 15 and pressure testing has revealed the cement plug is effective. The company said operations are now underway to replace the Deepwater Horizon drilling rig's failed blow-out preventer so work to complete a relief well can resume. BP estimates, depending upon weather conditions, that mid-September is the most likely date by which a relief will be put in place. -- Written by Joseph Woelfel >To contact the writer of this article, click here: Joseph Woelfel >To submit a news tip, send an email to: email@example.com.