British, alternative and rare pronunciation of r

There is a British way of pronouncing r which is possibly only English and that does not seem to leave much of a trace in the literature on pronunciation. It can be heard here at 6′ 30” in the word "majority". Would someone have details on that type of r?

It is a voiced consonant but is it a tap? Is it a trill? What is the IPA symbol? How does this sound compare to the Spanish r (so called rolled r)? Can it be called similar to it?

Isn’t it used less and less? Is there an apparent reason for the decreasing usage?