The date will have to be put back according to a Daily Mirror article from 23 Jan under the headline :
“Brexit has already been cancelled - and here's why they're not telling you”

There just won’t be enough parliamentary time to conclude the bills that need to be passed before March 29 .
“Of the 14 new bills required for Brexit - on things like animal welfare, money laundering and haulage - just 5 have been passed since the referendum.
Of the 9 remaining, the one closest to being finished is the Trade Bill - and the House of Lords just voted to shelve it because it lacked detail.”
That defeat in the Lords means that Britain is now unable to move to World Trade Organisation rules in the event of a no deal Brexit.
https://www.mirror.co.uk/news/politics/brexit-already-been-cancelled-heres-13896286