TL;DR - Yes upgrade system.
To expand because I am sure that's why you are here...
The panel is obsolete so no parts are available. As an aside, I am surprised your keypad is still functional, most I see now you can hardly read the screen or press the code in with ease.
Vo-Comm uses PSTN, you will not have this. The new router will probably have an ATA as you say but you will likely get issues with using this and it be unreliable, the same reason most fax machines are in the bin.
Virgin just want you to switch and deal with the issue later, but in fairness all newly designed systems should either be radio i.e. SIM card or IP i.e WiFi/Ethernet as options, be that private reporting or monitoring.
Even if you did it try connecting to the ATA and you were fortunate enough to have it work somewhat reliably, it would only take some router upgrade or power outage and it may stop working.
You will be responsible for making sure the ATA works and has line voltage so the Vo-Comm can dial, your PSTN provider currently do that -- with ATA if the router is powered off or crashes; then no line/no message.
These types of private reporting are not too reliable, so you may not care about it only working some of the time, there is no polling so who knows if it will work when you need anyway.