The bill has now passed the House of Commons. It will not come into force immediately on Royal Assent to allow for careful implementation.
Here is a link to the article in the Law Society Gazette: https://www.lawgazette.co.uk/law/no-fault-divorce-to-start-in-autumn-2021/5104682.article?utm_source=gazette_newsletter&utm_medium=email&utm_campaign=No-fault+divorce+in+2021+%7c+Legal+aid+support+%7c+Systemic+racism_06%2f18%2f2020