Firstly, let me make it clear that this is a murder mystery/conspiracy thriller set (partially) on a submarine and NOT a documentary about submarines, the navy, or nuclear missiles. As such there are inevitable inaccuracies and dramatic licenses taken (as they are in every legal drama, medical drama or police procedural). If you didn't like Line of Duty because it wasn't 'realistic' enough perhaps this one is not for you. If, however, you are able to suspend your belief for a few hours you might enjoy what seems to be a well written and superbly acted thriller.
***Mild spoilers***
In the modern way, Vigil opens with not one but two, big dramatic events that propel the plot forward. We are then given a somewhat silly plot contrivance to get DCI Amy Silva (a superb Suranne Jones) onto a Trident class submarine for three days in novel setting for the classic locked room murder mystery. The submarine feels suitably claustrophobic (although not enough for some of the previous reviews) and all the crew appear to be hiding something. Back on Land, DC Kirsten Longacre (Game of Thrones Rose Leslie), a former lover of DCI Silva's, investigates the naval barracks and some nearby anti-nuclear missile protesters.
The first episode had some heavy lifting to do introducing the characters and setting but the twin strands of the plot were intriguing, made even more so by that fact that Longacre was able to send messages to Silva but not the other way around. Aside from the use of a few tropes (tortured detective with a Past, big organisation closing ranks, etc) I found the show thrilling with precise camera work and skilful direction. Suranne Jones really is magnificent and Shaun Evans standouts as one of the few nice guys on the boat. If the show can continue to draw out performances from its excellent cast while keeping the plot afloat (!) then it should be a thrilling ride.