The chances are you are ringing main reception for them.
Having a look at their
website I noticed they use geographical numbers in the range 0207 235 7xxx. The fax number 0207 235 7112.
Therefore, try ringing another number in that type of range (eg 0207 235 7110) and when they answer just ask them is this the consumer advice line? They may say "yes" in which case you're lucky but likely they'll say "no" in which case just say to them sorry could you transfer us please as it was your reception/switchboard that transferred me in the first place to this wrong department.
If they don't transfer you (or lie and say they can't) then try another number nearby.
Another way I found that sometimes works and that is phone a nearby number like 0207 235 7110 and when they answer ask them if its the Consumer Advice Line when they reply "no" then ask them "sorry about that. Do you have their extension number?" The extension number will likely be 4 digits so just dial 0207 235 xxxx (xxxx being the extension number).
Let us know how you get on!