In the UK, one shocking source of work insecurity is the zero-hours contract (basically, you have no guaranteed income but have to be available whenever your employer feels like it). The EU has nothing to do with that, in fact most EU countries have banned the practise [1] but the British government refuse to do anything it in the name of 'labour flexibility'.
These same people are now claiming that leaving the EU, which offers important protections to workers rights through the treaties and the European Court of Human Rights, will magically solve problems they created and sustain themselves.
[1] https://fullfact.org/law/zero-hours-contracts-uk-europe/