Ah Birmingham Airport, how many times have I legged it for a train from you? Honestly, the chances of making it are pretty slim. I certainly wouldn't depend on it, especially if you have to pick up tickets as well. All going peachy you have 33 minutes in there (allowing for doors closing), which is enough time to cover the distance to the train even from the most Siberian of gates if you know the airport well, but realistically, just about . A minute or two delay, here or there will quite easily add up. Any flight delay will gobble that half hour up, another plane not leaving the gate in time will cost you, just missing the shuttle to the station will cost you, getting through the scrum exiting into the airport will cost you, getting off the plane will probably cost you. My minimum comfort time in Birmingham to a train would be 45 minutes and at that I would expect that on balance I will miss the train more times than I will catch it.