Can anyone tell me whether the router provding the VOIP service has to be the one that is directly connected to the ADSL line/socket?

Our network consists of several routers, only one of which is connected to the ADSL socket. I'd rather not switch them round unless I really have to as there are a lot of NAT settings that I'd have to re-do, and it has a very beefy firewall that I'd like to retain.

It may not matter.
But, what does matter is that your firewall/routers must provide port forwarding of SIP ports 5060 (or 5060-5065) and RTP ports (Linksys ATA's require ports 16384-16482).
Some services, like Skype, can get by with only ports 80 and 443, but will perform better when opening other ports (an optional Skype setting).

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cqVoIP
www.cqvoip.info

Ambriel,

As long as your NAT is set up properly, and your firewall is forwarding the proper ports you should be fine. Keep in mind that not all VoIP carriers are the same. What works on some may not work on others. For example some VoIP carriers prefer if your NAT is turned off as they handle it from their end to your equipment, while others will work whether the NAT is on or off. Ports; some carriers require many ports to be opened for udp while others require only one, or different ones. Always check with your carrier and compare and contact their support to find out if there is anything they can do.

- Tom Bradshaw
Link2VoIP.com