I had cause to complain a few months back when some overseas call centre operative called me and tried to convince me to take a service I didn't want - and then just added it anyway and started charging me an extra £10 a month.
When I complained, I was told that VM do not have separate complains people. They said the complaints are dealt with by the staff who take the calls. After having to phone a second time, I got the money refunded, but the promised letter of apology never arrived.
I think the problem would be that if Virgin Media had a complaints department, it would have to be the biggest department in their sorry organisation - to deal with all the things their long suffering customers have good reason to complain about!