The body of Bernadette Fox, 57, of Brookhill Road, Bootle was discovered on Friday after her daughter Sarah Fox, 27, was found dead on Thursday at a nearby property.
Peter Fox, 26, was arrested at London's Euston Station at 07:50 BST on Monday.
Tests showed Ms Fox was asphyxiated and her daughter was stabbed.
A man arrested on suspicion of murdering his mother and sister on Merseyside has been detained under the Mental Health Act.