I don't think there really is a straightforward answer to this - as there can be some institutional difference.
Though I would in general be a little bit surprised if it were required.
For people who have obtained a UK BSc (it may need to be an honours degree), it is possible to directly progress to a PhD, provided you get a First (maybe also a 2.1) in the BSc. (No idea about a BA - and all related types of Bachelor's degrees.)
This definitely applies to at least 3 universities in the engineering field.
Now: If I am not mistaken, I believe that the majority of people who were "doing a PhD" with a non-UK-education background had a Masters Degree before starting a PhD. (During my time at a UK university.)
However, this wasn't neccessary a Master's Degree from the institution at which these people were working towards a PhD. (Though one person was on some integrated course which was a 1 years Masters followed by a PhD.)
In this context, it may be interesting to note, that the "Student Loans Company" (i.e. the state) will loan the funds for a Bachelor's degree, but not a Masters. A PhD is typically funded (unless one goes for the self funded option).
This means, that unless you have wealthy parents or an employer paying for it, a Masters Degree in the UK makes little sense if you plan to follow up with a PhD and going Bachelors -> PhD makes more sense.
If we now look at the rest of Europe, it is pretty commonplace to obtain a Masters Degree before commencing a PhD. (Though some countries may have some different routes, such as the old German "Diplom" and the French Engineers that may lead to a PhD/Doctorate.)
And if you want a definite answer, the only method is to check the requirements on the university's website, as only they will be able to give you a definite answer.