Just to respond to the first half of your post...

I'm going to do my best to answer this in good faith. But let me just start by suggesting that... it's not really a fair question. A person isn't supposed to have to prove a negative in a rational discussion.

A claim was made - namely that the SNP had a significant impact on the election result south of the border (it's somewhat self-evident that they had an impact north of it - I don't think that's in question!) They "created divisions that allowed the Tories in", according to the original claim.

But a claim like that isn't just personal political opinion (of which this forum is filled, and that's totally legitimate), it's also an historical assertion. It's saying "this (controversial) thing... happened". And when you make a statement like that - on a forum where such things are discussed and challenged - it's not unreasonable to imagine that it's up to you to provide some evidence.

If I respond with "I haven't seen any evidence for that. Indeed most of the analysis suggests it's just not true", then it doesn't suddenly become incumbent upon me to prove the evidence does not exist. As I say; it's not up to someone to prove a negative.

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All that said, let me explain exactly why I think the SNP did not have a significant influence on the English vote. And also why I believe there's a compelling argument that even if Labour took every SNP seat, the UK would still have a tory government.

And look, I'm not saying we should instantly reject as mad or stupid or biased the claim that the SNP had an effect. As we know, the tories did use the Scottish Nationalists as a stick to beat Labour (though we'll have to agree to differ if you say it was "almost to the exclusion" of everything else). So it's reasonable to ask - after the election - whether that strategy was successful. Did the SNP, in fact, influence the outcome in England? Did they "allow the tories in?"

Firstly to political analysis. The witterings of columnists do not a "proof" make, but every single thinkpiece I read after the election came to (roughly) the same conclusions about why Labour lost. I didn't read a single one at the time to suggest that the SNP played a major part in the voting intentions of English people.

To refresh my memory I did a quick search on the phrase "factors in outcome of 2015 UK election" and skimmed the first 10 news results. 8 of them literally don't mention the SNP (except when specifically discussing Scottish results of course); one suggests the SNP probably had a negative effect on the Labour campaign and claims Miliband himself blames them for his defeat, and one mentions the SNP specifically to dismiss them as a factor.

Even the article that lays some of the blame at the SNP's door is really just saying that Labour failed to counter the tory PR... which once again is far less about the SNP than it is about Labour's inability to communicate effectively with the electorate (hint: the main reason for that was because they had nothing worth saying, and it's that fact that makes Miliband want to cast around for someone else to blame - but that's a discussion for another day).

Anyway, I'm not going to link to every article that doesn't blame the SNP, but they range from The Guardian (even The Letters page!) to The Telegraph to the New Statesman and beyond.

You will - of course - find outliers... columnists who will blame the SNP. But if you read the analysis - right, left and centre - it tends to uncannily reach a near-consensus. And it's not that the SNP had a measurable effect.

Because if we move from political to psephological analysis - there are clear reasons for the larger than expected tory majority. This is a decent article. But there are literally dozens of bloggers out there who have crunched the numbers and presented the data.

The collapse of the LibDems - and the fact that the tories appear to have taken the vast majority of their seats - is probably the single biggest factor that pre-election polls failed to fully account for. That factor alone likely accounts for a tory lead over Labour almost equal to the number of SNP MPs! On top of that, the UKIP vote hit Labour hardest in marginals, while it hit the tories hardest in safe seats. You would need a seat-by-seat analysis to fully explain that one; but I'd be willing to bet the farm on the SNP not being a crucial variable there.

Obviously Labour lost a large number of Scottish seats; and if the tory majority had been within that range, this discussion might be different. But the tory majority in England alone is more than twice the total number of Scottish seats.

As you say yourself - "the only evidence (you) can offer" for the SNP being a measurable factor in this English near-landslide is a tory PR campaign. Might I suggest that the links and analysis I've provided trump that? And that just because the tories shout loud enough about something, it doesn't automatically mean it's a real issue that will affect the real world?

If you're still convinced that the SNP are significantly responsible for the tory government, based on zero evidence and a tory PR campaign... then we'll just agree to differ.

And another thing...!

Yes, back again. I'm genuinely sorry if it looks like I'm unfairly jumping on your post. That's not my intention. But there was something about your second paragraph that was bugging me, but I couldn't quite put my finger on it. I kind of alluded to it in my previous post; but it's definitely worth its own post.

Firstly let me just say that just because a political party thinks a certain strategy will play to their advantage, does not mean it actually will. History is littered with bad campaigns that backfired badly.

Much more importantly though... I've realised that your argument basically runs like this:

The tories campaigned, partly, using a "vote Labour, get the SNP" strategy (to use your words). As I've argued already; there is no evidence that had a significant impact on the English vote. But let's say for a minute that there was. Let's imagine that a post-election poll suggested that large numbers of would-be Labour voters in key Tory/Labour marginals were influenced by that campaign.

So because of the Tory "SNP campaign" the UK now has Cameron as PM.

Except, even that does not demonstrate (or even imply) that the SNP are the cause of that vote transfer. It demonstrates that the tory PR / propaganda was successful. It says absolutely nothing real about the SNP, unless you want to argue that Tory advertising can be considered generally truthful?

To make a very relevant analogy, drawn from the same election... much of the UKIP campaign used "immigrants" as a bogeyman in much the same way the Tories used the SNP. Right? Does that say anything truthful or relevant about immigrants? Or does it speak to the nature of UKIP?