You can install a package resolvconf, which will modify the way
/etc/resolv.conf is built up at system boot.
sudo apt install resolvconf
You can then create or modify a file
/etc/resolvconf/resolv.conf.d/tail. If you put in this file a line
nameserver 220.127.116.11, this line will be added at the end of
/run/resolvconf/resolv.conf at boot.
/etc/resolv.conf will now be a symbolic link to this file.
Almost two years after posting my answer I came across https://bugs.launchpad.net/ubuntu/+source/ppp/+bug/1778946 which explains exactly why merely installing
resolvconf solved a dns problem I had at the time. I feel I have to share this here.
Although my answer addresses the question in a proper way, indeed a
warning should be added that, if you want/need to do this, probably
something else is wrong. This was already stated by @intelfx at the
time, 127.0.0.53 should work by itself.
According that bug report, after a pptp VPN goes down,
resolv.conf is restored with the wrong access rights.
ping ubuntu.com does not work,
sudo ping ubuntu.com does. Installing
resolvconf solved it, because it takes over
resolv.conf, restoring it with correct rights. Changing
systemd-resolve settings is no solution in this case, since the bug is in
ppp. But an alternative, maybe simpler solution is
sudo chmod a+r /etc/resolv.conf after VPN down. And this can be automated by putting an executable script in /etc/NetworkManager/dispatcher.d with contents:
if [[ "$1"="ppp0" && "$2"="vpn-down" ]]; then
/bin/chmod a+r /etc/resolv.conf
In all cases the contents of
resolv.conf do not change.
And, yes, I know pptp must be avoided because of security issues, but at the time I thought of it as a good excercise for an ubuntu newbie. I imagined it would work out of the box. Little did I know that it would give me a headache, as diagnosed so well by @intelfx.