It appears extraordinarily unlikely that conscription would return to the UK. Per
this article, it sounds like the rantings of one specific hawkish general and not at all the sentiment of the nation or in any way consistent historically.
Even if there was a need for additional troops because of increased hostilities, nations with volunteer militaries see major increases in volunteers in times of crisis or war. There was a big bump in the US, for example, after 9/11. There's little chance that conscription would become necessary.
Article Five of the NATO treaty states that if an armed attack occurs against one of the member states, it should be considered an attack against all members, and other members shall assist the attacked member,
with armed forces if necessary. There is also no obligation to defend a NATO country who initiates hostilities. So, there is no requirement that any NATO country commit troops to support others unless deemed necessary following aggression against them. More commonly, we see financial and technical support with weapons, etc...
The world can be a scary place right now, but a lot of that is because we have the unpleasant privilege of watching things unfold in real time. Imagine the terror in the hearts of every citizen of the world if we were watching Chamberlain negotiate with Hitler, or Kennedy talk FDR down from the Cuban Missile Crisis on 24/h cable channels and Twitter. I've become of the opinion that where world affairs are concerned, it's none of my business! I can't do a thing about any of it, so I need to just push it aside as if it's the intimate details of my neighbor's home life - better left behind closed doors and shut off TVs!