The Digital, Culture, Media and Sport Committee urged the government to publish a draft copy of promised legislation by the autumn.
It follows suggestions the Online Harms Bill might not be in force until 2024. The group's chairman said tech firms could not be left to self regulate.
Committee member Julian Knight said that there was no legislative architecture put in place, and we are still relying on social media companies' consciences.
"This just is not good enough. Our legislation is not in any way fit for purpose, and we're still waiting. What I've seen so far has just been quite a lot of delay."
Google and Facebook have said they have invested in measures to tackle posts that breach their guidelines.
However the report has already been welcomed by the children's charity NSPCC, which said the committee was right to be concerned about the pace of legislation and whether the regulator will have the teeth it needs.