Why did Churchill order the destruction of the bombes?

Something else to think about. As of the end of the war, Britain was in horrific economic shape, a situation which lasted for a few decades (not just because of the war, also because of policies around currency). The cost to break a thing is much lower than the cost to perpetually store and secure a thing.

Remember that rapid developments in general computers just after WWII rendered the specialized code breaking machines antiquated within a few years anyways. To keep them around stored somewhere, where someone could stumble upon them, would only unnecessary increase the chance that England's code breaking capabilities became know to other powers.

The destruction of the Colossus code breaking computers was a more significant thing, I gather the reasoning was the if the machines were retained other powers would pursue such technology. Britain had their own cipher machine typeX, there was some fear that if the cipher breaking machines became general knowledge then other powers would develop it and be able to read Britain's coded cipher machine communications. If the code break machines were retained they would be much more likely to be discovered, where if they were broken up, and their activities during the war would be harder to discover than if there was a continuing active group working with the machines.

Britain by this decision and suppression everything as an official secret and the breakup of the boffins responsible, threw away much of the British work in early computing, putting British computing back at least a decade when it could have been very much a world leader.

Colossus

TypeX machine

As per a few comments here: They weren't all destroyed. Reading a few books on the times there's strong hints that at least some capability was retained - both Bombes and more advanced equipment.

The Brits captured many Enigma machines and also the more advanced Lorenz (if memory serves) which they could also break. Both were either used by/sold to allies including the Russians and of course monitored by the Brits because we're excellent at being devious.

Again, dragging info from comments, very few people knew anything about any of this stuff up to the 1980's so there was no theatre in destroying it. I suspect they destroyed stuff at Bletchley and a few other places purely as they were only temporary during WW2 (or had way more machines than they needed), and retained or re-built the same or better at more permanent / suitable locations staffed by security service regulars rather than the assembled wartime staff who were dissipating back to regular life.

It's true Churchill basically banned further development at home after the war for security purposes, and handed a lot of research & secrets to the USA by way of offsetting the vast wartime debt. IIRC R.V.Jones says something along the lines of "He (Churchill) gave it all away far too cheaply" and felt he'd put the UK at a major disadvantage. (Most Secret War)

Edit to add:

The true details of all this have been very slow to come out. As mentioned above, Churchill was paranoid about the whole thing and pushed hard to bury it after the war, even to the extreme detriment of further R&D.

Given that Enigma, Bombe, Colossus etc. were only revealed 30+ years later, and some of the finer details from Bletchley have only come out in the last decade or so, anything that had any utility to the security services post-war (EG the Lorenz stuff) could still be under wraps. It's not hard to imagine some derivation of that kit being used well into the cold war (BT still had plenty of Telex lines running well into the 1990's). Apply a 30+ year embargo on that and we may not know the full story for another decade or two.

Additionally, it's easy to imagine that all of the stuff worked on by civilians during the war was deliberately destroyed so that they all went home believing it was all dead & buried, rather than spirited away for further use. By that point, the Americans had copies of the kit and we were all sharing mountains of intelligence etc.

If you, as a nation, have the capability to decode communications, then why give that up? This is independent of whether or not the Enigma machines were destroyed -- that ability should, if nothing else, discourage others from even trying, or at least give a head start in case someone did try to use encrypted communications.

The knowledge that your encryption is broken only leads to stronger encryption.

Enigma was broken because it was flawed, both in design, but also in operational use. But those flaws were not fundamental and could be corrected. If people knew about those flaws, and that they could be turned into a practical attack, they'd fix them. If they think it's secure, they'll stick with the status quo: it's cheaper.

The flaws in Enigma were not hard to fix, but you can't fix what you don't know is broken. B-Dienst, the German intelligence service, was both overconfident about Enigma's security, and greatly underestimated their enemy's codebreaking ability. Primarily they judged others based on their own attempts, and their attempts were lax because they considered Enigma unbreakable.

They took solace in the large number of permutations. They did not conceive their enemy might exploit flaws to reduce the possible permutations, nor develop machines to run through them. Developing a special machine to crack codes was a brand new idea, previously it had been done by hand and cleverness, and the existence of a Bombe would send cryptographers scrambling to reassess their algorithms.

In fact, Enimga was fixed during the war... by the Allies. The British Typex is basically an improved Enigma. The US had the ECM Mark II / SIGABA. They were modified to be compatible as the Combined Cipher Machine. They're all rotor cipher machines contemporary with Enigma. While they had flaws, they were not as flawed as Enigma.

We see this played out today: even though better algorithms are available, older cryptographic algorithms are kept in service even as theoretical attacks are developed. It takes a practical attack before it's abandoned in droves. For example, SHA-1 has been crumbling for years, but it's only in the last few years that it's finally being phased out.

Similarly, people are becoming more aware of the greatly increased parallel processing power available. For example, a dozen GPUs can give an attacker the sort of parallel processing power for a few thousand dollars that previously would have cost millions. What would previously have been a purely theoretical attack might now be practical. Security folks use that knowledge to reassess which practices are safe and which are not.

Most people who worked on Enigma code-breaking didn't know the real name of the system, or the scale of the effort being made. That contributed to the secret of the breaking of Enigma being kept until the 1970s.

So "appearing less threatening" is a non-issue. The few nations who know, already know, and have better cryptography. Nobody else knows. The information really was tightly held. A USN submarine officer, John P. Cromwell, deliberately went down with a sinking submarine to avoid capture by the Japanese and possibly being forced to reveal the secret.

The Allies sold captured Enigma machines to third world countries after WWII, because they were widely believed to be secure. This is a normal level of dirty tricks for this field. The amount of material from the new Enigma users was going to be much less than from Germany during the war. Most of the bombes were not going to be needed.

If you destroy most of them, or even the whole lot if there's a better replacement, then if the secret leaks, you have a credible claim that you can't read that code any more. You also avoid the costs of guarding and maintaining large, complex and very secret machines.