I could only find 'would rather' but not 'had rather' in the dictionary http://www.ldoceonline.com/dictionary/rather
Not a teacher.
Student or Learner
1) I would rather take tea.
2)I had rather take tea.
Which one is correct/more common?
I know the contraction for both is: 'd.
2 is incorrect.
Have tea is very common in BrE too.