I wish - and I bet most politicians who have played the immigration card - wish that such a simplistic view held the slightest validity.
Except it's not a "UK container issue", it's a route that's been used and is being used throughout the EU. In the week of the deaths in the UK, there were reports of similar seizures in Germany and IIRC Greece and Holland. It's been commonly reported for years - EU wide. It is not the politicians (of any colour), unless you wish to blame the lack of detailed inspection of every individual lorry and container, i.e. remove all contents, inspect every package, measure for hidden compartments etc. Which given the level of imports and global trade we all indulge in would push severe delays to every product and import. Probably enough to start killing migrants often, and ruling out import/export of perishables as even vaguely viable.
We'd probably have to go back to pre-war open cargo to have even the slightest chance of retaining an import/export economy for perishables.
The migrant camps getting into the EU, and relocating from one EU country to another (e.g. Calais) have gone from strength to strength through clearances, crackdowns and multiple administrations. The issue has been there decades.
> E-verify and crackdowns on employers of illegal immigrants
...is already there, particularly harsh, and applied in more than just one EU nation. Yet has not had the blind bit of effect on immigrants. The problem stems from a Vietnamese paying $20-50k to someone in their country for their "opportunity" for a better life in Paris, London, Berlin - and presumably NYC, Washington and San Diego too...
Many of whom they have paid for a lifelong debt, threats to family and have bought themselves into modern slavery and perhaps a life in something outright illegal or the sex trade. If you're shipped into the underground economy a crackdown on employers and e-verify is targeting exactly the wrong thing, only ever destined to find collateral.
It remains a growth industry in all of the developed nations. Walls and internment camps barely register to discourage while much of the pressure is external profiteering... A complete redesign of import-export capitalism might. No more coffee, tea, bananas and other "exotica" for US and Europe then.
Not to mention the increase in wars and climate impacts forcing people who otherwise wouldn't to consider migration. Those external pressures just keep on rising...