Corby Town Council wants more action after the contaminated land scandal of the 1980s.
An emergency law has handed control of the UK's only remaining plant making virgin steel to the government.
The UK government has taken control of the Scunthorpe plant under emergency powers - the SNP believes the oil refinery at Grangemouth should also be nationalised.
The rare Saturday sitting of Parliament includes speeches by MPs from across the region.
A source said the issues being discussed by government officials and the firm remain unresolved.
British Steel has warned materials needed to keep blast furnaces operational in Scunthorpe are running out.
The UK government is considering nationalising the Chinese-owned firm which employs 2,700 people.
Business minister Sarah Jones says all options are open in response to calls for nationalisation.
