If the public school has a gifted coordinator, I would call her Monday and ask for a meeting. Try and convince her to met your child and/or talk to your tester. Coordinators say all kinds of things before they meet your kid, but often start singing a different tune after they see your child.
I would definitely do this. I can't tell you how many times we heard "we just don't do that" until they met my kids and then they agreed with me!

Too, I'd be careful that, even if the conversation started casually talking about your child, they understood that you wanted them to seriously consider your proposal. Perhaps bring the WPPSI results with you so they know that you aren't "one of those parents" who thinks their kid is the smartest kid ever. In our situation with my youngest DS, we were in an acceleration meeting for our DD when the principal of the school casually commented that our youngest DS would probably need some accomodations as well. We laughed and agreed and the GT coordinator heard us. We kind of thought the school might initiate something. But that was all that happened until we came to them and specifically said what we wanted done. To them, it was just a casual, non-committal conversation until we brought it up pointedly. In the end, after our specific requests, he was tested and then skipped K.
You've already done half the work for them by giving them the WPPSI results!
Good luck and welcome!