Things that access web during bootup

[#1]

I've got AVG8.5 and Ad-aware AE on my pc. Do these access the web during bootup, to get things such as updates? If they do, is there any way I can stop them, so they only access the web when I tell them to? I seem to be going through my monthly web allowance at an incredible rate just lately. Last month I used it in two weeks. Until this year, I rarely used my monthly allowance. I realise an extra 2GB doesn't cost much, but I'm not trying to economise. I'm just trying to understand what has changed, and how to control it.
Regards and thanks

[#2]

Dont think its those two as I havnt stopped web access and only just go over 2 Gb for the month  (mind you am upping it at this moment watching Live Video from Pirate BBC Essex on all weekend

[#3]

The quickest way to see whats happening is to download tcip view free from
http://technet.microsoft.com/en-us/sysinternals/bb897437.aspx
and run it on startup. Its shows all connections so you can then see if or what is downloading.
I assume you dont use wireless or if you do its secure and no one is using it for free?