"It is shameful that Theresa May has threatened to withdraw security cooperation from our closest neighbors and allies," Farron said.
"Completely irresponsible to threaten, gamble or bargain on national security. This isn't a threat to EU, it's a dangerous act of self harm," tweeted Yvette Cooper, the chair of the House of Commons Home Affairs Committee.
In comments to Parliament, May did not comment directly on the security references in the letter. But the text appeared to speak for itself:
"If, however, we leave the European Union without an agreement the default position is that we would have to trade on World Trade Organisation terms. In security terms a failure to reach agreement would mean our cooperation in the fight against crime and terrorism would be weakened. In this kind of scenario, both the United Kingdom and the European Union would of course cope with the change, but it is not the outcome that either side should seek. We must therefore work hard to avoid that outcome."
The message carried extra clout in an era when the fight against militant networks and other threats depends heavily on intelligence sharing and cross-border investigations.
On some matters, such as intelligence sharing, Britain works with countries across Europe on a bilateral basis, and those relationships would remain. But Britain is also a part of the EU security services such as Europol, the European Union law enforcement network.
"Security is too important to be used as a bargaining chip and this will backfire in any negotiations, which rather than building up alliances will leave Britain even more isolated," said Farron.
A spokesman for the prime minister said that she was simply being candid.
"The prime minister's words speak for themselves," he said. "It's a simple fact that if we leave the EU without a deal then the arrangements which we have as part of our EU membership will lapse."
Amber Rudd, Britain's home secretary and an ally of May's, rejected the idea that security and an overall trade deal were being linked.
"There are two separate items here . . . It's the same paragraph but it's not in the same sentence," she said, when the section from the letter was read out to her on Sky News.
"There is no threat. I'm amazed that's even being thrown up," she said. "We need to have an agreement, so that the UK can continue to help keep the European continent safe and that the European continent can continue to help keep the UK safe. This is not going to be traded, this is something that has to be negotiated."
