Speculation, and a question: Perhaps the city-state civ is desperately trying to make a settler, and a boat to put it on, so as to avoid annihilation. If it doesn't have a spare military unit to send out, and waltz into your bait city, that may explain it.
Question: If England has declared war against Tiny-ville, aren't they building more units and getting stronger ... which will make them harder for *you* to conquer? What's your motivation for keeping England on a war footing while you get ready to invade?
Those are two good reasons (city-state making settler; or doesn't have more than one military unit). I guess I could blockade their port squares. That may make them change to making a second military unit. Whatever they might be making it's going to take them a long, long time, cause all their land territory is polluted, they only have the city shields.
(This is Deity setting)
The reason I want England in two Alliances with me, against the two city-states (that they actually can't touch), is so England won't attack me. So far, it's worked. With the Alliances, and then Embargos, and trade, England is in a good mood with me. I've determined, as long as there are other nations for it to war with, it's not going to try to conquer me.
England being in a war status is nothing new. They've been in a constant state of war at least 90% of the entire game (in 2000 AD), and for this last half of the game without any peace intermissions. They just eat up nations nonstop. I'm convinced that if I was only remaining nation, no matter what, they would attack me. I don't think the AI can determine they can't reach the city-states and must attack me to win (victory condition war only).
Right now, besides to two city-states I have surrounded, there are only 3 nations, including myself, and England is at war with the other (Babylon), and they are both burning up eachothers' military units. England bombs the hell out of them for years and years. I'm about to attack the weakened Babylon now, and hopefully maneuver to take most of it's territory. I already have 25% more territory than England, but am still weaker militarily and science-wise (England's already at the end of the science chart). Because I will have 25-50% more territory/cities than England, the more time I have, the more I can close the gap between us, and the easier it will be for me to beat England in a final battle. Obviously you don't have to be very far behind an AI to beat them militarily.
So, through the game, whether England is making guns, or saving gold, (and they're always at war without my influence) my overriding priority is keeping them from attacking me.