You've answered your own question.
It sounds as though the bath tap is faulty, or more likely, someone has made a balls of fitting a flexi connector to it, which is kinked.
Have a look under the bath panel, and see if there is an iso valve partially open.
It sounds as though the bath tap is faulty, or more likely, someone has made a balls of fitting a flexi connector to it, which is kinked.
Have a look under the bath panel, and see if there is an iso valve partially open.