Not tube stations, where Bayswater/Queensway and Bank/Cannon Street are very high on the 'ridiculously close' list. But actual railway stations which, for geographical or historical reasons, were built almost adjacent.
I can do you an official list courtesy of maptwiddler extraordinaire Alasdair Rae. Last week he uploaded a spreadsheet of all 2573 National Rail stations and the distances from their nearest station. Corby, for example, is exactly 11.015km from Kettering. St Albans Abbey, meanwhile, is exactly 1.213km from St Albans City.
It doesn't always work out reciprocally. For example Harpenden is nearest to Luton Airport Parkway but Luton Airport Parkway is nearest to Luton, not Harpenden. Highbury & Islington is the closest station to Essex Road, Canonbury, Drayton Park and Caledonian Road & Barnsbury, but is itself closest only to the latter. Alasdair's drawn lots of maps to show how all this works, which was the overall point of his excellent blogpost. But you can also use his spreadsheet to confirm the UK's closest railway stations so that's what I've done.
And the majority of these very-close stations, it turns out, are in London. Given the density of the population that's perhaps not a surprise.
Outside London the closest pairs of stations are as follows...
124m St Budeaux Ferry Road ←→ St Budeaux Victoria Road (Devon) 132m Heath High Level ←→ Heath Low Level (Cardiff) 216m Wigan North Western ←→ Wigan Wallgate (Lancs) 243m Dorking Deepdene ←→ Dorking (Surrey) 251m Rice Lane ←→ Walton (Merseyside) 280m Upper Warlingham ←→ Whyteleafe (Surrey) 360m Ebbsfleet International ←→ Northfleet (Kent) 378m Birchgrove ←→ Ty Glas (Cardiff) 379m Liverpool Central ←→ Liverpool Lime Street (Merseyside) 400m Maidstone Barracks ←→ Maidstone East (Kent)
But there are twelve pairs of stations in London which are closer than 400m.
And the closest of all are these two.
93m Catford ←→ Catford Bridge (Lewisham)
The UK's closest railway stations are Catford and Catford Bridge, located just 93m apart on either side of the River Ravensbourne. They were built in separate years by competing railway companies so there was never any incentive to connect them. Also one's on a viaduct and one's at ground level (plus there's a river inbetween) so linking them later was never a sensible option. It takes less than a minute to walk from one to the other, I tried it yesterday, and that is ridiculously close.
If you're standing in the ticket hall at Catford it takes exactly the same amount of time to walk up to platform 1 as it takes to walk across to platform 1 at Catford Bridge. I actually measured the distance as 80m, not 93m, but Alasdair's calculations use the 'official' location of each station which isn't the same as measuring between the closest points. Whatever, 93m is so close that it even beats Bayswater/Queensway and Bank/Cannon Street, making Catford/Catford Bridge genuinely the closest stations in the UK.
A particularly stupid thing to attempt, therefore, is a rail journey from Catford to Catford Bridge. That'll be why if you attempt to buy a ticket from one to the other the system refuses. Even the member of staff in the ticket office can't do it, their machine won't sell one. But it is of course possible to use Oyster or contactless between the two, however contorted the journey, so a fare does indeed exist. That fare is £2.50 off-peak and £2.80 peak, the same as a normal zone 3 single fare, despite the fact you can only make this journey by straying into an additional zone.
I have a travelcard so when I attempted this journey yesterday it didn't charge me anything. I took one train north from Catford to Nunhead, another train east from Nunhead to Lewisham and a third train south to Catford Bridge. If you want to see how all this manoeuvring works and how much it costs, plus what everything actually looks like, you should watch the seminal Geoff Marshall video "You Can't Buy A Ticket from Catford to Catford Bridge". But he took 42 minutes whereas I completed it in 32, because it turns out a special timetable on a Sunday with major engineering works is a particularly efficient way of making all the connections.
The second closest pair of stations is here.
136m West Hampstead ←→ West Hampstead Thameslink (Camden)
There are in fact three separate stations located very close together along West End Lane, two of which (Underground and Overground) are called West Hampstead while the third is called West Hampstead Thameslink. Plans to properly merge all three stumbled due to impracticalities and cost, which does indeed leave two not-quite neighbouring National Rail stations.
Being somewhat perverse I also attempted to make a direct rail journey from one to the other rather than do the easy 90 second walk. I started at West Hampstead and rode the Overground east to the next station with a direct National Rail interchange which was Highbury & Islington. From here I took the Northern City Line to Moorgate, then switched to Crossrail for one stop to Farringdon and finally caught a Thameslink train up to West Hampstead Thameslink. And it took ages, mainly because I just missed my first connection and just missed my third connection so I spent half an hour waiting on platforms.
My total journey time from West Hampstead to West Hampstead Thameslink was 1 hour 21 minutes, which is an average speed of 0.06mph as the crow flies. I could have done it faster by passing through a gateline and I could have done it faster by using the tube, but that would have gone against the spirit of the challenge. I could also have done it faster on a day that wasn't a Sunday with major engineering works, because what helped me in Catford totally hindered me here. But mainly what I learned is that I shouldn't have tried it at all, save to acquire some ridiculously impractical bragging rights.
The third closest pair of stations is these two.
214m London Kings Cross ←→ London St Pancras International (Camden)
It's surprisingly easy to travel between these two rail termini by train, you get a train up to Finsbury Park from one and a train back down from Finsbury Park to the other. I did not bother to try this because I had learned my lesson.
Here for completeness is the full list of closest pairs of railway stations in Greater London.
93m Catford ←→ Catford Bridge (Lewisham) 136m West Hampstead ←→ West Hampstead Thameslink (Camden) 214m London Kings Cross ←→ London St Pancras International (Camden) 244m Dalston Junction ←→ Dalston Kingsland (Hackney) 264m Battersea Park ←→ Queenstown Road (Battersea) 315m Walthamstow Central ←→ Walthamstow Queen's Road (Waltham Forest) 322m Forest Gate ←→ Wanstead Park (Newham) 328m Hackney Central ←→ Hackney Downs (Hackney) 333m Canada Water ←→ Rotherhithe (Southwark) 352m Manor Park ←→ Woodgrange Park (Newham) 375m Seven Sisters ←→ South Tottenham (Haringey) 380m London Waterloo ←→ London Waterloo East (Lambeth)
