Copyright in a University of Hull PhD thesis belongs to the author, unless a prior arrangement has been made with a funder or sponsor. (University of Hull Student Contract 2018-19, #7.2).
Before graduation, the successful PhD candidate is required to deposit a digital copy of their examined thesis (including any corrections) in Hydra, the University's open repository for research. The British Library harvests theses from Hydra for Ethos, a searchable collection of over half a million theses from UK participating institutions.
The author may choose to withhold their thesis from public view (an 'embargo') for up to five years, if, for instance, it contains commercially sensitive information, or potential for adaption into a book or journal article(s).
If your thesis incorporates material written by you which has been published already (for instance, a journal article), bear in mind that you may have transferred your copyright to the publisher. Check the terms of your Agreement to Publish, and contact your publisher for permission to republish the material if required. If permission is not granted, you can choose to embargo the material concerned, by depositing it as a separate file.
University of Hull students can find further information about submitting and depositing their thesis on the Doctoral College Sharepoint site.
English copyright law allows anyone to quote from published material, "for criticism and review or otherwise", providing your use is "fair dealing" and you attribute the quote to the original author. You may "quote" excerpts from audio and visual imagery as well as text.
You do not need the rights-holder's permission for an attributed quote. There is no need to identify the copyright status or rights-holder in your bibliography or in-text citation.
There's no limit to the length of your quote, although you should be prepared to justify why you needed to reproduce the amount that you chose in order to make your point. It's arguably not "fair dealing" to rely on the Quotation defence when reproducing material which could have a market value in its own right, such as a poem, photograph or artwork.
You should be particularly careful when reproducing other people's figures, illustrations or photographs in your thesis, as the copyright status may not be clearcut.
If non-commercial use of the image is permitted, ensure that you credit the rights-holder in your image caption (the Creative Commons wiki has a useful guide to captioning CC images). If not, you will need to contact the rights-holder for permission to reproduce their work in your open access thesis - look for a request form or email address on the host platform or publisher's website.