British universities refer to what we call dissertations as “doctoral theses.” The British Library has a thesis service. According to that web site
The British Thesis Service gives you access to the full text (by purchase) of more than 170,000 doctoral theses, mainly from the 1970s to the present day. Almost all UK universities make their theses available through the Service....Microfilm copies or bound paper enlargements of most theses are available for sale.
There is an online order form and you may make the purchases with a credit card. See their site for more information, including which universities participate and how to use the BL Intregrated Catalog to find a thesis. Except for those doctoral theses held by the Center for Research Libraries, British theses cannot be requested through ILL. For those held by CRL, a Thesis Declaration Form (TDF) must be filled out by the requestor. ILL has the form and they will fax it to CRL with your request.
For more information, contact ILL.