Many thanks for your patience. I am afraid there are no laws which state that after working for someone for a specific period of time or because you have been paid holidays, etc they have to take you on permanently as an employee.
In fact a person's legal rights in the workplace will mainly depend on their employment status. However, establishing your employment status is not an easy task and there is no single test that can be used. It is usually irrelevant what a person is labelled as by their employer because their status would depend on the overall employment relationship, not on what they referred as.
Following years of case law, a number of established factors have generally been accepted as a reasonably accurate way of establishing whether someone is an employee or self employed. The courts would still use some of these to get an overall picture of the employment relationship and determine the person's employment status.
Some of these factors can be viewed here:
By following the link you may get a good idea of what your employment status is, although it is worth noting that these are still only an indication and only a court can provide a definitive answer. They are nevertheless useful to use in negotiations with the employer.
So even if you were labelled as self employed but the nature of the relationship meant that you were treated as an employee, your rights will be those of an employee.
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