They add: "Buried in the agreement is the offer of a 'new, deep and special relationship' with the EU in defence, security and intelligence, which cuts across the three fundamentals of our national security policy: membership of Nato, our close bilateral defence and intelligence relationship with the US and the Five Eyes intelligence alliance.
"The first duty of the state, above trade, is the security of its citizens.
"The agreement abrogates this fundamental contract and would place control of aspects of our national security in foreign hands. Please ensure that your MP votes against this bad agreement and supports a sovereign Brexit on WTO rules, without payment of ransom."
Writing for the Telegraph today, Sir Richard says: "The key to my argument lies in the agreement's offer of a 'new, deep and special relationship'. This sounds a harmless enough form of words. But in reality, it would serve to cut across the three fundamentals of our national security policy.
"Were the UK to participate in EU defence frameworks in the way Mrs May proposes, it would entail onerous conditions. These would likely include full adherence to EU defence policy, and the high likelihood of having to become a 'rule-taker' on intelligence, space, financial contributions and the European Defence Agency.
"It is surely not acceptable for us to agree to such terms when, during all our time as an EU member, we have managed to avoid such obligations."
Pro-Brexit defence chiefs have long claimed the agreement amounts to the UK continuing spending taxpayers' cash to prop up Brussels defence and foreign projects - including the controversial "EU army".
It comes after secret recordings in March revealed Whitehall officials boasting to EU diplomats that Brexit would be like a Kit Kat with chocolate covering ties to Brussels for years.
In their November 29 letter, Sir Richard and Maj Gen Thompson argued that May's deal was the "exact opposite of the people's instruction to take back control", saying it surrenders national security by subordinating UK defence forces to military EU control and compromising UK Intelligence capabilities.
Arguing it places the vital Five Eye Alliance "at risk", the letter called the European Commission an "undemocratic organisation" that had "demonstrated how untrustworthy and hostile towards the UK" it is by "using the Irish border as a weapon".
Urging May to leave the EU on WTO terms, it warned the public to "ignore the hysterical demonisation of this course of action by the current Project Fear", insisting "no risks are greater than the Withdrawal Agreement's terms of surrender".
No 10 insisted there would be "no subordination" and that "every sector, nation and region would be better off than in a no-deal scenario." It denied the £39 billion was a ransom, saying it was a "fair settlement of our obligations as a departing member of the EU".
Sir Richard said the reply showed No 10's "worryingly poor understanding of the issues", adding: "No 10's immediate response to our letter showed we had touched a raw nerve."
- Telegraph Media Group
