Forty years ago, London University was still offering degree registration to "external" students, who might be living anywhere in the world. To prepare themselves for the London exams, many studied at local institutions; but it was also acceptable for external students not to study at any institution but to study "privately". Some of these "private" students had private tutors, while others studied wholly on their own, without any tuition, and after being registered for the required period of time they presented themselves in a London or London-accredited examination room and sat the exam papers. Fees were paid both for registration and examination. For many decades, the availability of degree examinations to private students was considered one of the special features of London University.
I am not asking for recommendations, but are there any British universities nowadays that register and examine students who study wholly on their own?
Note that I am not asking about degrees by "distance learning" in which coursework is required and tuition bought from and given by the degree-awarding institution, or by an institution accredited by it, although it is possible that the kind of degree registration I am asking about might be considered a sub-category of distance learning.
Considering how cash-strapped and/or financially savvy British higher education institutions tend to be nowadays, you are extremely unlikely to find such a programme set available anywhere in the British isles.
In the days of online distance learning and MOOCs (massive open online courses), there is probably no valid reason for an institution to grant degrees for free.
The rationale for charging fees for distance learning is that registering with a degree programme, you precisely do not 'study wholly on your own', but you benefit from a wide range of resources, not the least digital, to have access to the latest scholarship, in addition to the expertise the local staff 'holds' themselves.
If you are based outside the UK, your natural first port of call to find an answer for a question of this nature would be the British Council; they are the experts to advise globally about UK educational and cultural opportunities.