As an Australian, I (sarcastically) don't like being compared to kiwis! ;) I was just in USA and americans told me they had trouble understanding what I was saying (but I do have a thick aussie accent compared to most and its deeper) But i think its because Americans don't watch alot of Aussie TV or movies, so they aren't used to the acccent. I didn't have trouble understanding them, however sometimes they would say words that are not commonly used here (ex: slippers = thongs, icebox = fridge). Kiwi's in my opinion sound a bit south african (ex: hey bru). Candian's sound like americans but have a softer accent. Cockney is a strong accent, but I can understand it.

Accents in english, as a whole, don't change the meaning of the sentence. English doesn't have any dialects. That's why I believe English became a universal language, since it could be understood easily. Take any Asian language and then add in the regions (plus history, culture etc.), you then have both dialects and accents that can be very different. Like, my grandmother is orignally from a small village (no one knows where) and she speaks a dialect of Mandarin that no other Chinese person can understand. Also take the differences between Kansai-ben and Toyko-ben, Seoul and Busan.

Yes, they can. In the situation you describe, with everybody speaking at normal speed and avoiding slang and regional colloquialisms, these five people will understand each other without any difficulty. The five different accents would not cause a problem. There may be the occasional word or expression which one of two of them will find unfamiliar, but this is unlikely to impede mutual comprehension. The speakers will usually be able to guess from the context what the odd unknown word means. 

I know that you haven't asked this specifically, but my guess about whether or not the five people would be able to identify each other's accents is this:

1. The Londoner will only able to tell the difference between the American and the Canadian if the New Yorker has a strong NYC accent. He/she may assume that the Canadian is from another part of the USA, and will probably not be able to tell the difference between the Aussie and the Kiwi accents.

2. The New Yorker would recognise the Canadian as a fellow North American, but may not be able to tell for sure where he/she comes from. There are a few tell-tale signs of the Canadian accent, such as the 'ou' sound and a softer, lower tone, but Americans have told me in the past that they still don't always know if someone is Canadian or not. The American may struggle to distinguish between the three other accents. It is widely recognised that the London accent has more in common phonetically with the Australian accent than with other accents of the UK.

3. The Kiwi and Aussie would be in the best position to identify the accents. They would, obviously, be able to tell the difference between their own respective accents. NZ and Australia receives TV and films from all over the world, and so they would recognise the London accent, the New York accent, and would have as good a chance as anyone of identifying the Canuck.

As mentioned above this group of people would have no problem at all understanding each other. It is the same language, just with different pronunciations of certain words and different slang. But then someone from the East End of London would not speak in Cockney rhyming slang around people who they knew would be unfamiliar and confused by it, they would speak in Standard English. Rhyming slang can be difficult to understand even if you're from the UK as well!

All of the accents you mentioned are pretty easy to understand, there are other English accents which are much more difficult. The Glasgow accent and Newcastle accent are two that come to mind. Northern Irish accents can also be difficult to understand as the accent can be quite harsh. I think people non-native to the UK would struggle with these three more than the London one purely because they will have had a lot less exposure to them. Personally I can identify what part of the UK someone is from due to their accent pretty easily due to lots of exposure. I can tell an American accent, but as for what part I would have no real idea unless it was really obvious like the stereotypical NYC accent. Again for the other countries, I could guess the country from the accent but not a specific region.

As for your question about the BBC, there isn't a standard 'British' accent per se. For starters the UK is made of four separate countries, England, Scotland, Wales and Northern Ireland which all have different accents, and there are many different dialects within these four countries as well. The accent most BBC newsreaders have nowadays is sort of a generic Southern English accent, which is quite easy to understand. So yes it is probably a good guide for pronunciation purposes, but to be clear the majority of people in the United Kingdom have a different accent to this.

Unless a speaker's accent is very thick (and in your hypothetical situation, it isn't), then we should have no problem understanding each other clearly.  In a real situation, we would avoid using slang anyway and use standard English. This means we would definitely understand each other clearly... and to be honest, I believe you're over-thinking this. We don't speak <em>that</em> differently. ;)

As an Australian (in Australia, our English-speaking media is quite diverse, which means we do hear different accents often), I'd have no problem understanding any of the speakers you mention. How well I can identify their accents would depend on how accustomed I am to accents from that region.

I suspect you chose a New York accent because it's meant to be a hard American accent to understand, and Cockney because it's meant to be a hard British accent to understand, as well as Australia and New Zealand because they're geographically isolated, but people with these four accents might have an <em>easier </em>time understanding each other than other English speakers. Australia, New Zealand and the New England part of the US (which includes New York and Boston) were all settled by speakers of the old Cockney accent, so the accents/dialects are much closer to each other than you'd intuitively expect. New York English, Modern Cockney, Australian English and New Zealand English have each been influenced by American English, RP, Irish English and Scottish English respectively, to varying degrees, but they ultimately stem from the same dialect.