Boris Johnson has chaired a cabinet meeting and will later lead the daily coronavirus briefing for the first time since his return to work.
No 10 said the PM, whose fiancee gave birth on Wednesday, will update the UK on the "fight against this disease and the steps we are taking to defeat it".
But political editor Laura Kuenssberg said he was unlikely to give "chapter and verse" on lifting the restrictions.
No 10 also faces the deadline for its target of 100,000 daily virus tests.
Health Secretary Matt Hancock pledged to reach the goal by the end of April. The latest figures show it reached just over 52,000 coronavirus tests on Tuesday.
A scientist advising the government on testing, Prof John Newton, said he is "pretty confident" the government will hit the target but warned there will be a lag in the data.
He said it would not be clear whether the target had been reached until the end of the week.
However, Justice Minister Robert Buckland admitted the target might not be met by the end of April.
The government's chief scientific adviser Sir Patrick Vallance and chief medical officer Prof Chris Whitty will appear alongside the prime minister at Thursday's briefing.
Mr. Johnson, who has just recovered from Covid-19, returned to work in Downing Street this week but missed Prime Minister's Questions on Wednesday following the birth of his son with his fiancee Carrie Symonds.