The wording of the relevant legislation seems important here. The EU (Withdrawal) Act 2018 specifies that exit day is March 29th, 2019, but (20(4)) that the Brexit Minister may amend that definition to "ensure that the day and time specified in the definition are the day and time that the [EU] Treaties are to cease to apply to the United Kingdom".
So, on that reading, until an alternative date was agreed with the EU, the government would have had no power to table the necessary amendment, because it was conditional on the Government and the EU coming to an agreement first.
All this mess could, and should, have been avoided by not specifying a date, which was an attempt to placate Hard Brexiteers, and has anyway now failed utterly in all of its aspects. And, of course, has had the ironic effect of handing even more power to the EU: Parliament, in an attempt to ensure that we left this Friday, deliberately passed legislation that attempted to tie its own hands, and required the EU to untie them for us.
Make no mistake, though, this situation over March 29th and the Statutory Instrument was entirely due to Hard Brexiteers in Parliament.