A downhole tool includes a bore isolation valve, a sensor configured to receive to a downlink signal, an annular pressure sensor, a valve actuation mechanism coupled to the bore isolation valve and responsive to the downlink signal, a pressure relief mechanism configured to provide a negative pressure pulse signal indicative of the annular pressure by venting fluid from a bore of the tool body, and a battery. A method includes drilling a well with a drill bit coupled to an on demand annular pressure tool initially in a deactivated mode, and activating the tool by a downlink signal when fluid flow out of the annulus drops below the fluid flow into the well to close a bore of the tool, pressurizing the drill string, holding pressure in the drill string, measuring annular pressure with the tool, and sending a negative pressure pulse signal indicative of the annular pressure.