That's topologically speaking, counting stations rather than measuring distance.
For example Mill Hill East is one stop away from an interchange, Battersea Power Station is two and Richmond is three.
But we can do a lot better than that.
The winner, if you only count tube stations and no other mode of transport, is the northern end of the Bakerloo line. Harrow & Wealdstone is 13 stops away from Paddington which is the first station where you can change onto a tube train to a different destination, and that's the longest dead end on the network.
In second place is what I initially thought was going to be first, the eastern end of the District line, where Upminster is 12 stops away from West Ham. Before the Jubilee line was built it would have been 15 stops away from Mile End so would have been the winner, but since 1999 Harrow & Wealdstone's been the longest tube dead end instead.
The tube's longest dead ends 13 stations: Paddington → Harrow & Wealdstone 12 stations: West Ham → Upminster 9 stations: Camden Town → Edgware 9 stations: Stockwell → Morden 8 stations: Earl's Court → Wimbledon 8 stations: Finsbury Park → Cockfosters
n.b. If you count dotted lines as interchanges then the Bakerloo loses its crown because of a connection at Kenton, but I've decided that post-2018 dotted lines shouldn't count.
n.b. At present the Heathrow branch of the Piccadilly line is a 10 station dead end because the T4 loop is closed, but that's temporary so I haven't included it.
But there are lines on the tube map other than the tube, so what happens if we consider those too? For example Harrow & Wealdstone is now only 7 stations from the Overground at Willesden Junction, and Upminster is no longer a dead end once you consider the runty line to Romford.
What are the longest dead ends on the tube map? (including Thameslink, trams, Dangleway, the whole shebang)
The winner is now Watford Junction to Willesden Junction, which is again 13 stations but this time following the Overground rather than the Bakerloo line. Joint second place goes to the Northern line's Edgware branch and Crossrail from Hayes and Harlington out to Reading, both of which go 9 stations without interchanging with anything else. The only 8 station dead end is the Cockfosters end of the Piccadilly line and the only 7s are on the Central Line, trams and DLR.
n.b. The DLR used to be in a strong second place, with Lewisham a full 11 stops from Canary Wharf, until Thameslink was shoehorned in.
n.b. Considering the wider London rail & tube map doesn't extend things much because London doesn't have many long National Rail dead ends, but you could argue Hertford North is 10 stops from Alexandra Palace.
And we can do dead ends on London bus routes too.
Which routes have the most consecutive bus stops before you can change onto another TfL route?
The winner, unsurprisingly, is the TfL route that extends the furthest outside Greater London, the 465. It goes further than this map shows, indeed all the way to Dorking, a terminus which is somehow 35 stops away from the first alternative route in Chessington. Second place goes to the K3, another Surrey-serving service linking Esher and Surbiton, and third place to the Slough-bound 81, the sole TfL bus west of Heathrow.
Routes staying within Greater London have much shorter dead ends, as you might expect.
n.b. Numbers of bus stops may vary inbound and outbound, so take these figures with a ±1 pinch of salt.
n.b. Yes, technically you can change between the 142 and 258 anywhere on the run out to Watford Junction, but I'm still counting it as a 19-stop dead end.
And let's just flog this idea into the ground by considering the longest dead ends on the National Rail network.
The Cambrian line to Pwllheli is by far the longest dead end (discounting the heritage railway that links it to Blaenau). The Far North line to Thurso would be second if only it didn't branch to Wick at the far end. The Tarka line to Barnstaple used to be 12 stations until last month when the line to Okehampton reopened.
Again I was expecting longer dead ends than this, given how many railway lines there are across the country, but the National Rail network is generally very good at linking back onto itself.
It turns out connectivity is king, and only a few routes branch out all on their lonesome.
n.b. I've probably counted some of these wrong and maybe missed a few, sorry.
n.b. I've probably not applied exactly the same rules in the same way you would have done, not sorry.