It depends how you play Ganton and off what tees. For the 2003 Walker Cup the 17th was a 250-yard par 3 but the 6th was played as a 470-yard par 4, giving a yardage of 6894 against a par of 71. The Medal Course (as the members play it) has the 6th as a 449-yard par 5, but the 17th as a 252-yard par 4, giving a total of 6,734 yards for a par of 73. The members, then, only have two par 3s - 5th and 10th.
Irvine is another course with only two par 3s. It was used for this year's final qualifying for the Open Championship at Royal Troon. I seem to remember that a contributor to this site was going to caddie for someone at Irvine. I'd love to know what they thought of the course. I have a feeling that the other course in Irvine - Ravenspark - also has only two par 3s.
I'm sure I can find other courses in the UK, but I can't be bothered at this moment!