The following procedure works for Ubuntu 18.04 (Bionic Beaver)

I. Reinstall the ifupdown package:

# apt-get update
# apt-get install ifupdown

II. Configure your /etc/network/interfaces file with configuration stanzas such as:

source /etc/network/interfaces.d/*

# The loopback network interface
auto lo
iface lo inet loopback

allow-hotplug enp0s3
auto enp0s3
iface enp0s3 inet static
  address 192.168.1.133
  netmask 255.255.255.0
  broadcast 192.168.1.255
  gateway 192.168.1.1
  # Only relevant if you make use of RESOLVCONF(8)
  # or similar...
  dns-nameservers 1.1.1.1 1.0.0.1

III. Make the configuration effective (no reboot needed):

# ifdown --force enp0s3 lo && ifup -a
# systemctl unmask networking
# systemctl enable networking
# systemctl restart networking

IV. Disable and remove the unwanted services:

# systemctl stop systemd-networkd.socket systemd-networkd \
networkd-dispatcher systemd-networkd-wait-online
# systemctl disable systemd-networkd.socket systemd-networkd \
networkd-dispatcher systemd-networkd-wait-online
# systemctl mask systemd-networkd.socket systemd-networkd \
networkd-dispatcher systemd-networkd-wait-online
# apt-get --assume-yes purge nplan netplan.io

Then, you're done.

Note: You MUST, of course, adapt the values according to your system (network, interface name...).

V. DNS Resolver

Because Ubuntu Bionic Beaver (18.04) make use of the DNS stub resolver as provided by SYSTEMD-RESOLVED.SERVICE(8), you SHOULD also add the DNS to contact into the /etc/systemd/resolved.conf file. For instance:

....
DNS=1.1.1.1 1.0.0.1
....

and then restart the systemd-resolved service once done:

# systemctl restart systemd-resolved

The DNS entries in the ifupdown INTERFACES(5) file, as shown above, are only relevant if you make use of RESOLVCONF(8) or similar.

The Netplan team has posted an official answer on their FAQ here:

How to go back to ifupdown

...

On a running system, netplan can be removed by installing ifupdown and configuring /etc/network/interfaces manually as users have done before.

At install time, a user can opt to use ifupdown by preseeding netcfg/do_not_use_netplan=true. This is done by adding the preseed line to the command line when booting the installation media (i.e. at install media boot menu, press F6, type ‘e’, and add to the command line).

See Nuxwin's answer for more complete instructions.

The answer of Nuxwin is great and almost complete, I'd just add the lines:

rm /etc/resolv.conf
ln -s /run/systemd/resolve/resolv.conf /etc/resolv.conf

This will make sure that the resolver can be updated by the DHCP-client, like it was before when using interfaces.

(I would have added this as a comment but somehow one need 50 reputation to post a comment)

Why not just configure with netplan?

Well, as it is configured in 18.04-Desktop, it is a single line handing over control to all interfaces to NetworkManager.

While that is probably suitable for 95% of users, remember that NetworkManager is only run once you are logged in to a session.

Should you want your machine to act as a server/desktop, for example start serving files to local machines, acting as VNP server, etc... or anything "fancy" before anyone is ever logged in, just by the simple fact it is on, you will have trouble with how it is configured in standard 18.04-Desktop.

Of course, the alternative would be to use the server-Netplan configuration, which, as far as I have read (not checked by myself), hands control over to systemd-networkd instead. In this case you'd better learn how systemd does things as a replacement of the old System V init.

Should you go this path, you still have to make change to the netplan yaml, since on a desktop version the control is given to NetworkManager.

Why not just remove netplan:

$ sudo apt remove netplan
$ rm -rf /etc/netplan

Once for all!

The key is knowing that cloud.init is the real control program.
That being said the line in the netplan config file "optional: true" is mandatory.
Knowing that made it easy.

I just removed 01-network-manager-all.yaml and copied it to /root/save/. Then put a known good config in place instead of it, 50-cloud-init.yaml: its contents follow:

network:
  version: 2
  renderer: networkd
  ethernets:
    eports:
      match: 
        name: enp*
        optional: true
  bonds:
    bond0:
      interfaces: [eports]
      addresses: [192.168.2.5/24]
      gateway4: 192.168.2.1
      nameservers:
        addresses: [127.0.0.1, 8.8.4.4]          
      parameters:
        mode: 0          
        mii-monitor-interval: 100

Then reboot and it should be working fine.

The known good config came from Configure bonded 802.3ad network using netplan on Ubuntu 18.04.

According to this answer, the solution is to remove all operational .yaml files: Ubuntu 17.10 disable netplan

I wouldn’t remove anything without backing up. We can do so easily by simply moving the files aside. First, locate the files:

sudo updatedb
locate netplan | grep yaml

On my 18.04 system, it appears that the only operational file is /etc/netplan/01-network-manager-all.yaml. Let’s move it:

mkdir ~/netplan
sudo mv /etc/netplan/01-network-manager-all.yaml  /home/user/netplan

...where user is your user name.

Now check to make sure the file is truly gone:

ls /etc/netplan

Now make your additions to /etc/network/interfaces as required.

Reboot.

Any improvement?

Footnote: The exact process to do this is hard to find. We may need to refine a bit as we go.