An interesting little anomaly - Realtime Trains, as demonstrated in the attached photograph, suggests that the distance from Bedford to Bedford St Johns is just 18 chains, or under a quarter of a mile. However, as per Google Maps, it's probably closer to three quarters of a mile or so, being a fair bit longer than Wallasey Grove Road to Wallasey Village at 25 chains. I know that St Johns has been re-sited, but its new location is closer to Bedford Midland than the old station would have been, not further away, so how does this come about?
Additionally, it's a three-minute journey time, which, at 18 chains, would mean an average speed of 4.5 miles per hour, which doesn't particularly strike me as realistic.
Back on topic, a couple from the North London Line that I haven't yet seen mentioned are Brondesbury and Brondesbury Park (35 chains on RTT and timed for one minute start-to-stop), while Highbury & Islington to Canonbury (which is not ELL-exclusive so arguably doesn't count as a metro under the rules in post #90), also timed for one minute start-to-stop, is 33 chains. Brondesbury to West Hampstead is just over half a mile, at 41 chains.
Ardrossan Town and Ardrossan Harbour have been mentioned upthread (38 chains on RTT), but it's probably worth throwing in Ardrossan Town to Ardrossan South Beach at 42 chains. Anderston to Glasgow Central is 34 chains (also timed one minute start-to-stop), while Anderston and Exhibition Centre are also shown as 41 chains apart (although I'm vaguely aware that the track layout there does odd things so I'm willing to be corrected on that one: I've never been to Glasgow).
As for the Valleys, obviously the Coryton line has got much of the attention and rightly so, but honourable mentions ought to go to Dingle Road and Penarth (35 chains), Danescourt and Fairwater (40 chains), and Fairwater and Waun-gron Park (35 chains), as well as Bargoed and Gilfach Fargoed, and Aber and Caerphilly (both 48 chains).
The Severn Beach line has been mentioned upthread - the distances on RTT are shown as 37 chains Portway Park and Ride-Shirehampton and 36 chains Redland-Montpelier. I haven't yet seen Lawrence Hill and Stapleton Road mentioned, at 46 chains, but they possibly deserve an honourable mention too.
At 45 chains I shall also throw in a mention for Godley-Newton for Hyde on the Glossop line. If we're counting closed stations, then Godley East (closed 1995) was around halfway between Godley and Hattersley (which themselves are 66 chains apart), surviving with a parliamentary service after the former's opening for a few years.
A final mention for the following from Merseyrail: Orrell Park-Walton (30 chains), Bootle New Strand-Bootle Oriel Road (33 chains), Green Lane-Birkenhead Central (34 chains), Moreton-Leasowe (38 chains), Conway Park-Hamilton Square (39 chains), Overpool-Little Sutton (41 chains), and Port Sunlight-Spital (45 chains). (This is ignoring the central loop as I think that's already been covered on this thread.)
(All mileages taken from Realtime Trains.)
Attached image is a screenshot from Realtime Trains showing the distance from Bedford to Bedford St Johns quoted as 18 chains.