I have the same problem my cpu(celeron g1840) has usage 50% and more (not reported as a system process) because of network activity to sites like keeton.canonical.com, ftp.bit.nl and others.
This is what's happening:
Active Internet connections (w/o servers)
Proto Recv-Q Send-Q Local Address Foreign Address State
tcp 0 0 192.168.178.18:44458 ams15s30-in-f14.1e:http TIME_WAIT
tcp 0 0 192.168.178.18:36860 haetae.canonical.c:http TIME_WAIT
tcp 0 0 192.168.178.18:56900 stackoverflow.com:https ESTABLISHED
tcp 0 0 192.168.178.18:44448 ams15s30-in-f14.1e:http TIME_WAIT
tcp 0 0 192.168.178.18:39302 ftp.bit.nl:http TIME_WAIT
tcp 0 0 192.168.178.18:55386 keeton.canonical.c:http TIME_WAIT
tcp 0 0 192.168.178.18:36874 haetae.canonical.c:http TIME_WAIT
tcp 0 0 192.168.178.18:39326 ftp.bit.nl:http TIME_WAIT
tcp 0 0 192.168.178.18:39300 ftp.bit.nl:http TIME_WAIT
tcp 0 0 192.168.178.18:44582 ams15s30-in-f14.1e:http TIME_WAIT....
and:
Active UNIX domain sockets (w/o servers)
Proto RefCnt Flags Type State I-Node Path
unix 2 [ ] DGRAM 16324 /run/user/1000/systemd/notify
unix 7 [ ] DGRAM 9851 /run/systemd/journal/socket
unix 18 [ ] DGRAM 9858 /run/systemd/journal/dev-log
unix 2 [ ] DGRAM 9862 /run/systemd/journal/syslog
unix 3 [ ] SEQPACKET CONNECTED 278774 @0001b
unix 3 [ ] DGRAM 9844 /run/systemd/notify
unix 3 [ ] STREAM CONNECTED 672328
unix 3 [ ] STREAM CONNECTED 17853
unix 3 [ ] STREAM CONNECTED 20773 /run/systemd/journal/stdout
unix 3 [ ] STREAM CONNECTED 280847
unix 3 [ ] STREAM CONNECTED 17269 @/tmp/.X11-unix/X0
unix 3 [ ] STREAM CONNECTED 73730 /var/run/dbus/system_bus_socket
unix 3 [ ] STREAM CONNECTED 19760
unix 3 [ ] STREAM CONNECTED 670256 @/dbus-vfs-daemon/socket-w2sHGKfi
unix 3 [ ] STREAM CONNECTED 672329 @/dbus-vfs-daemon/socket-19luYW2N...
I tracked it down up to:
32411 _apt /usr/lib/apt/methods/http enp2s0 0.572 20.516 KB/sec
31916 _apt /usr/lib/apt/methods/http enp2s0 0.547 20.490 KB/sec
The appcenter is indeed causing the problem, the solution to stop the appcenter from auto starting worked for my system.