Surely if your dad has been here for 8 years on a work permit, he must have Indefinite Leave to Remain in the UK? Did he not apply for Indefinite Leave to Remain for you as well?
If not, you may now struggle to show that you are a dependant on him as you are no longer living with him and presumably he is not supporting you financially. Your best option if you are wanting to study at university in the UK is to apply for a Tier 4 visa, this would however prevent a gap year from being possible. There is not really any way to remain in the UK without getting a visa in your own right now and aside from a Tier 4 visa, unless you can get a job and a Tier 2 visa.
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