Shoreditch High Street

This has been discussed several times before. The Central Line will not get a Shoreditch High Street station at least until after Crossrail is built, maybe not until after Crossrail 2/Chelney happens.
The reason is that there is no capacity on the Central Line trains for any additional passengers in the peaks - already it is virtually impossible for many people to get on at Bethnal Green in the peak-flow direction, so the platforms at SHS would just get overcrowded during every peak time.
If Crossrail 1 relieves the Central Line sufficiently in this area, then I'm sure it will be considered at that point, as I believe the station was built with passive provision for such an interchange.
If it doesn't, but Crossrail 2/Chelney does, then I'm sure it will be considered at that point.
Until then you'll just have to wait unfortunately.

More detailed reasons have iirc been posted in one of the previous several threads on this topic, and I'm sure one of our expert thread finders will be along to link to it/them before too long.

From Quail Track Diagrams, Southern and TfL 3rd Edition

Mile End - Stratford 2.77km
Liverpool St - Bethnal Green 2.27km
King's Cross - Farringdon 2.05km
Bank - Waterloo 2.03km

with

King's Cross - Highbury & Islington 2.43km

So your only raise which works is Mile End - Stratford, which is quite far out, but King's Cross - Highbury looks like a good one too for zones 1-2

CULG gives from Ongar (0 point) Blake Hall as 2.97, North Weald 5.71 and Epping 9.85, making North Weald the furthest from elsewhere on the line both before and after Blake Hall closed.

Amersham-Great Missenden was (is?) 8.25km, and would appear to be the all time record holder.

I ran the Circle line route once in preparation for the marathon. In comparison to the rest of the Circle, Farringdon to KX is miles

Yep, I can't resist saying that farringdon to Blackfriars is the shortest though ! ;D

Yep, part of my old maintenance area so I regularly walked it, in fact I walked the entire Picc line both roads more than once and the tunnel sections multiple times. Apart from signal maintenance, mostly at the West end from Acton to Heathrow and South Harrow, I was also responsible for tunnel telephone wire cleaning for all Picc sections as I was also the line comms TO.

The entire T4 loop is roughly 5.3km but for signal maintenance it had to be done in three sections, T4 to Hatton cross, T4 to WY100 and T123 to WY1 in one tunnel and back to T123 in the other. At the time there was little more than two hours track time and often three signal maintenance teams would work in unison to do all the signal, tunnel telephone and tunnel lighting maintenance in a single shift but it could be graft as there was a lot for a two man party to carry. This did not include any point maintenance which was done separately on subsequent shifts.

Probably less far than Harrow-on-the-Hill to Finchley Road.

The tube map is actually a diagrammatic representation of the LUL network and does not claim to depict the actual geographical location of stations in relation to each other nor the actual physical distances between adjacent stations on the same line. Additionally stations actually geographically close to one another may not be indicated as such on the tube diagram. On the Piccadilly Line for example, the diagram indicates distance between Covent Garden and Leicester Square might be similar to the distance between Wood Green and Bounds Green. In reality, this is most definitely not the case.