score:4
Platform choice is key here. A and 2 are at opposite ends of their respective stations.
Platform A is in a bas*m*nt level of St Pancras. Here's an interactive map of St Pancras: you're in the top right corner (you might need to scroll right to find it).
You need to come up two levels, go through the ticket barriers, turn left and walk through the building, then cross the road. It's not unreasonable to allow five minutes to get from the door of the train to the door of King's Cross.
Once you've entered King's Cross, you're standing by platforms 9-11. Here's an interactive map of King's Cross - it's oriented the same way as the St Pancras map, and you're at the entrance of the new concourse right by Platform 11b, top right. Platforms 0-8 are in the other concourse, depicted at the bottom of the map, with platform 2 at the further end of it.
You have a choice of two routes: either (1) turn right just past the coffee stand, head up the escalator, turn left and follow the walkway round through the ticket gates and to the far end, where there's an escalator (and a lift) to take you down to the platform; or (2) walk diagonally across the concourse to the ground-floor ticket gates to the right of the ticket office, through the gates and to the far end. It's usually less crowded to take the upstairs route. Either way though, it's not unreasonable to allow five minutes. Also, bear in mind that train doors are usually locked a little before departure, and that you might need to allow time to find an allocated seat on the train from King's Cross.
As someone very familiar with both stations, I'd expect to make it from B to 2 in well under fifteen minutes - but I'd probably feel a bit nervous with a connection of less than ten.
Upvote:6
The two stations are on opposite sides of the same road. 15 minutes is a pessimistic estimate to get from a platform in one to a platform in the other, allowing for someone who doesn't know their way around, walks slowly, gets held up by crowds throughout, etc.