FDF,
Looking at GE I'd guesstimate that from the railway line to DSA terminal is approx 1km ... and I'd guesstimate that is a similar distance to the main concourse and gate 22 (if it's still there after all these years) of LGW.
And why would such an airline as KLM want to operate in/out of a "skin of the teeth" airport such as Sheffield City, and with restricted loads, when there is a full size "Sheffield" airport just up the road and around the corner?
When Sheffield City was open previously there was no nearby alternative but thereafter the MoD released the former RAF Finningley and, these days, there is a nearby and full sized airport alternative.