The current UK record is NOVA1 with 32Km, but it should be possible to get to 40km with rubber balloons, this is the aim of Ultrahab. To reach such a high altitude, larger balloons, a light payload (no phone, only radio), and low ascent rate is needed. This increases the risk of ending up in the sea, so multistaging (using 2 balloons at launch) is needed for a fast ascent through the troposphere.