The National Union of Teachers has voted for a series of fresh strikes, starting with a national walkout in June.
The action relates to a long-running dispute over pay, pensions and working conditions.
More top news
In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The star celebrated his 70th birthday with his family before attending a celebrity-filled bash held in his honour.
Douglas Carswell told ITV's Peston On Sunday he wanted to "support" the government as a "critical friend" but refused to rule out a return.