I suspect this is Billardiera fusiformis, which is climber with generally broader leaves than Billardiera heterophylla, which is usually a shrub.Both species occur in Canberra.
Now I am getting confused. Weeds of Australia https://keyserver.lucidcentral.org/weeds/data/media/Html/billardiera_fusiformis.htm says "While it is thought that both Billardiera fusiformis and Billardiera heterophylla are cultivated as horticultural plants, it seems that the majority of cultivated and naturalised specimens in Australia actually belong to Billardiera fusiformis. The most recent Victorian Plant Census reflects this by only recognising Billardiera fusiformis as being naturalised in Victoria. Therefore, it is highly likely that most, if not all, of the naturalised populations of bluebell creeper in other states are also attributable to Billardiera fusiformis, though they have yet to be re-classified as such." So I won't be able to compare with my neighbour's plant.
Weeds of Australia incorrectly generalised from the Vicflora notes. What they say about states other than Victoria is not true. They used one of Jackie’s photos from the south coast of NSW and called it Billardera fusiformis when it is actually heterophylla. Michael M and I went through the angst about this and checked all uploads on CNM at the time this problem came up. Both species definitely occur in the ACT. The Weeds of Australia fact sheet gives good diagnostics.