What I Did:
I installed Helm with
curl https://raw.githubusercontent.com/kubernetes/helm/master/scripts/get | bash
helm init --history-m
I ran into the same issue - exactly the same configuration as initial question: Ubuntu version: 18.04 Kubernetes version: 1.16
@shawndodo's answer didn't work for me. There were some issues with the tiller deployment and the tiller pod was not getting created at all!
I tried installing the from canary build as described in Helm docs - https://helm.sh/docs/using_helm/#from-canary-builds
helm init --canary-image --upgrade
This didn't work a couple days ago, but tried again (with newer canary build) and it worked today (20191005).
Whether I run into other issues now using canary build remains to be seen, but I got past the initialisation issue...