TfL state the distance from Moorgate to Barbican at 0.40 miles and the inter peak running time as 1.50 mins (this is 1m30 secs, not 1min 50 secs). The distance from Barbican to Farringdon is 0.32 miles with a running time of 1.51 mins.
The elapsed time from train to train on the clip is almost dead on three minutes. This means that even if the participants' run followed the (reasonably straight) route of the railway, they would have covered 0.72 miles in that time. This means they would have to be four minute milers (near enough).
Looking at it differently, using those running times and allowing one minute for the stop at Barbican, this means a train covered the 0.72 miles in 4 minutes 41 seconds (4.68 minutes). This gives the train an average speed of 9.2mph.
If the run between alighting from the train and joining it was straight and level with no impediments, a runner capable of a mile in about six minutes could make it. But clearly the route is not straight and level. And looking at a map, although there are some curves in the railway route (especially between Barbican and Farringdon) there is not a practical straighter alternative route above ground.
I have seen evidence of a similar feat performed between Earl's Court and West Brompton. However, this is a much shorter route (about a third of a mile) and the running route (via Warwick Road and Eardley Crescent) is almost identical (and in fact may be slightly shorter) to the route taken by the train. The participants may also have benefitted from the train being held briefly at Earl's Court. However I have no doubt that this claimed feat (Moorgate-Farringdon) is bogus.
