Until recently Jersey made a considerable amount of money hosting warehouses for companies like Asda, Tesco and Amazon who were exploiting Jersey's low tax, low VAT regime and customs union with the UK to import goods VAT free. This was possible because Jersey isn't in the EU and can therefore apply its own VAT rules (such as not applying VAT to anything worth less than £15) but is in a customs union with the UK which means VAT and duty aren't applied to goods imported from Jersey. The EU wasn't very happy with the arrangement because they get a cut of VAT charged in any EU member state so they ordered the British government to put a stop to it which of course they did.
Although the Channel Islands aren't part of the UK - they're Crown Dependencies - the British government can legislate for the islands. The Jersey and Guernsey governments both appealed to the High Court but lost and the British government put the Channel Islands-based operations of many large companies out of business overnight, putting many people out of work and damaging the local postal services.
It is hardly surprising that Channel Islanders might be questioning the value of their relationship with the UK given that the British government have systematically undermined their sovereignty, their economies and worked against their national interests by siding with the EU. It's a shame they don't have political parties in Jersey and Guernsey because I suspect UKIP would do very well!