ITV News understands the lorry carrying the 15 passengers belongs to a firm called Thermotraffic and that it stopped in Calais before reaching the UK.
ITV News producer Sandi Sidhu has tweeted:
I'm told that the lorry belongs to Thermotraffic came frm Europe and had stopped in Calais. It was supposed to be carrying general cargo
Police have said the vehicle "originated in mainland Europe" and that it "has been seized as part of our investigation".
More top news
The singer had been tweeting in support of migrants when she was bombarded with abusive messages.
Ministers are reportedly considering plans in a bid to lower inward migration.
In a tweet on Saturday, the US president didn't give a reason for his absence but said he wished"everyone well and have a great evening".