Two communities are claiming compensation and want Shell to clean up their land.
Shell said it is at an "early stage" in reviewing the claims and that the case should be heard in Nigeria. The Ogale community of about 40,000 people in Rivers State, on the coast of Nigeria, who are mainly farmers or fishermen, are some of the claimants.
Their case is being handled by law firm Leigh Day. Spills since 1989 have meant they don’t have clean drinking water, farmland or rivers, their claim says.
It points to a November 2015 report by Amnesty International which says four spill sites Shell says it planned to clean up are still contaminated.
The first court hearing is due on Wednesday at the Technology and Construction Court, which will determine if the claimants can can lodge a case against Shell’s Nigerian business, known as Shell Petroleum Development Company of Nigeria (SPDC).
Amnesty’s findings followed a 2011 report by United Nations Environment Programme (UNEP) which found water contaminated with oil by-products including benzene, thought to be a carcinogen. It suggested a clean up, but said a "sustainable recovery" of the area could take up to 30 years.
Shell says it has agreed a clean-up plan.