The UK is committed to leaving the current customs union when it exits the EU on 29 March 2019 and ministers are under pressure to agree soon on a successor arrangement amid divisions in cabinet.
He said Mrs May's "well-meaning options" on customs had been rejected by her Brexit war Cabinet and he doubted whether the Prime Minister could formulate a "successful" way forward on the issue.
Organised by the campaign group For our Future's Sake, the letter from 60 student unions says promises made by pro-Brexit groups have not been kept and that an estimated 1.4 million people were too young to vote in June 2016 but now deserve a say.
But May wrote in the Sunday Times: "You can trust me to deliver".
When asked on the BBC's Andrew Marr Show if he agreed with Johnson that the model is "crazy", Gove replied: "With the new customs partnership - Boris pointed out that because it's novel, because no model like this exists, there have to be significant questions marks over the deliverability of it on time".
The customs partnership would see Britain collect import duty on behalf of Brussels when companies buy goods from non-EU countries that are destined to be sold to buyers on the continent. And in return, my pledge to you is simple: "I will not let you down".
In their article, they wrote that a hard Brexit was economically irresponsible and "a path to a fantasy island" which would leave the United Kingdom with a "diminished standing in the world".More news: Trump to address Jerusalem embassy opening by video
"They do literally plunge a knife into the heart of government and particularly to the Prime Minister - because it is very much her fixed view, and that is what we stood on at the last election".
Last year, London put forward two options to ease cross-border trade with the European Union but, with Brexit looming, has still yet to make a final decision on which to pursue. "Of course, the details are incredibly complex and, as in any negotiation, there will be compromises", she said.
Brexiteers such as Boris Johnson are against Mrs May's preferred option of a "customs partnership", which is backed by Remain-voting ministers.
A second plan, known as "maximum facilitation" or Max Fac, would set up a looser relationship between the two trading partners and use technology to minimise disruption and border checks.
Starmer said: "We have said a comprehensive customs union with the EU is a necessary minimum".