In the abstract sense that lower wages are bad for the public at large, perhaps.

Against this we have to consider the lower cost of public works if undocumented labour is used, more stations built, more libraries and so on. We have to consider jobs onshored, such as in Toronto's sewing sweatshops; at least the wages earned are spent in the country where paid.

One can make a case that illegal labour is bad for the labourers but it may be that the dead cockle pickers would otherwise have been dead slave labourers at home; we can't say that they were worse off in the UK.

il·le·gal [ih-lee-guhl] Show IPA
adjective
1.
forbidden by law or statute.
2.
contrary to or forbidden by official rules, regulations, etc.: The referee ruled that it was an illegal forward pass.
noun
3.
Informal. illegal alien.

Many things are illegal drugs, speeding, theft and a host of other things regardless of if we agree with them.
Many of us work in our day to day jobs that are covered by some form of law be it minimum wage or industry standard wage. An employer cannot pay you less than the prescribed amount as that would be illegal.
How would you feel if someone came along and offered to do your job for less money that was below the legal amount. If your employer hired that person and put you out of a job would you then claim thats illegal.
Until it directly affects us as an individual or the job we do then we tend not to care about it being illegal.
Yes we can cherry pick certain things like speeding and try to justify our actions but if its illegal then usually there are consequences and if illegal by law there is usually a punishment.

I don't dispute that it is harder to immigrate legally to the US when compared to Canada.

Undocumented labour (as you put it) is a distortion to the economy. It effects wage levels, employability, safety standards, quality, labour standards and justice. It impedes planning it undermines efficiency measures. What happens when the construction firm using documented labour can't win any tenders because its bid is too high? Greece had a massive black economy with undocumented labour and in particular undocumented earnings. It's a slippery slope.

In Australia the press goes wild if 50 people turn up illegally on a boat. How they would cope with US or even UK numbers of illegals, I dread to think.

Is there an argument that having high levels of illegal workers lowers the wages for everyone?

Absolutely. Wage suppression is one of the main purposes of legal immigration, which is why Labour opposed EU entry for so long. Illegal must have a push-down effect on local wage economies.

Surely the concern in the US is the reverse, the economy is dependent upon undocumented labour; ending the supply now would force the price of goods up.

It would push both prices and wages up.

The Chinese cockle pickers had entered the UK having destroyed their passports. The Chinese government have a policy of not accepting returned nationals who do not have official documentation so, although the authorities were well aware of their presence, there was nothing that could be done to remove them from the UK. Detainiing them would have been an administrative exercise, and they'd have been released almost immediately.

Tragic case no matter how you look at it. The sad thing is there are probably dozens more people in such impossible situations.

Absolutely. I'd never decry anyone for trying to better themselves. We should never lose sight of the fact that 'illegals' are real people, who have real reasons for wanting to leave their countries of origin. We Westerners find it (relatively!) easy to pursue opportunities in other countries, but that's not necessarily the case for a lot of folks from the 'Developing World'.

So how many illegals are working in Canada who come from the UK, Ireland, Germany, the USA and a few other westernized countries?
What are the reasons for them leaving those countries is it because those countries are war torn oppressive style regimes and treat their citizens with no respect?

In these cases its all about the JOBS and if an illegal ends up taking your job are you OK with that?

No idea as to the figures regarding Western immigration, legal or otherwise.

I was really referring to the habit of demonising 'illegals' and specifically referring to immigration from the developing world. It's often the case that the only way that some folks can get into Western countries is to employ subterfuge. I expect that even legal immigration is not universally popular with many Canadians, many of whom could be doing the jobs that are being filled by members of this forum.

I don't think anyone is OK with anyone else taking THEIR job - regardless of status!!