Instead of looking at universities as teaching in pure quality in numbers, to answer your question it might be better to approach it from a different direction. Pure quality does not answer much - you can look at lists online anywhere which will tell you a series of abstracted statistics about the quality of each university, but as a student myself (but not a history student), I don't find those numbers actually have any real meaning. Infact, even worse, sometimes I find I sharply disagree with the rating given by the statistics. As such, it might be a bad idea to put too much weight into the rating systems you read online. When I was selecting universities for my degree in political science, I also ran the gamut of looking through lists of the best unis, asking people which was the best uni for me, and so on and so forth, but none of those routes were particularly informative to me or helpful in my decision. Instead, I will provide an alternative idea which might be more helpful to you which I wish I had inquired into when I was choosing universities.

What period of history and topic of history are you most interested in? All universities will have different specialities within their departments which will cater to specific views and topics due to the lecturers on staff. The courses at universities are decided by the actual areas the local lecturer's are capable of teaching to a good quality. If you inquire into this instead, you might find a university which provides precisely what you are looking for, instead of a university which has an 86 for 'student satisfaction' and a 94 for 'teaching quality'.

As such, I am going to ask you to change your question, which might see you get more help than you have so far. Share with us what it is you want to study in history at university, and then someone might be able to give you far more tailored assistance in narrowing down your options. The more information you can give on specific periods and topics, the more help that can possibly be given?

Additionally, instead of looking up the numbers and looking into useless open days for universities, my further advice would be to browse all of the university course listings for your chosen course. Under that category there should be listings of all of the current undergrad modules, which could help in your selection.

Basically, instead of just looking for the quantified 'best' university, which does not really exist, you should instead look for what you want out of a university.

Will it advance areas of interest which you want to pursue?

Does it offer a diverse array of courses?

Am I going to get what I am looking for in a history degree out of this course?

These are perhaps more useful questions for a student in preparation than "what is the best university?"