In case anyone finds this thread ever again, here is the solution that worked for me. There is a point during the chase where Magnus tells you "hurry, he's closing the gate" or something similar. If you kill the mime that is closing the gate, it will remain open, you'll go through it, and eventually end up in the alley where you get stuck. If you do not kill the mime before he closes the gate, Magnus will make a right turn to take an alternate route and you won't end up in the alley where you get stuck. That's what worked for me anyway.
Note: during the chase there is at least one Spy Tra