please empty your brain below

Brunel line? Because of the Thames Tunnel
Well in this house the New Cross to Dalston line is always referred to as the Hipster line.
another vote for Brunel
South East London line is probably a bit more accurate and also references the old South London Line portion, but might be a bit of a mouthful I suppose. (Perhaps, then, it could be SELLie to go with Still anon's "Nellie"!)
Brunel is my preference, although unlike the District and Metropolitan there is quite a short section that is common to all the lines, perhaps Brunel (Crystal Palace), Clifton (West Croydon), Eastern (New Cross), Saltash (South London Line).
The German part of my brain screams for standardisation rather the typically British muddle of names.

I'd therefore suggest OL1 for this line. DLR routes to be titled DL1+ etc..
In reality this is surely still the East London Line. However, as it goes to Croydon, and Captain Sensible sang a song about the place, let's name it after him, the Captain Sensible line. (Even if that leads it to be colloquially known by regular travellers by the name of his group)
The Brunel Line (in honour of the Thames Tunnel)
I would go for the Brunel Line as well. East London Line is a bit bland (and probably could be what the GOBLIN is called)
East London and Brunel are basically the only sensible naming (as opposed to lettering/numbering) options. And 'East London', while having historical pedigree, is indeed bland and if you go with that you might as well go with the banal, utilitarian, unromantic letter/number code.

So I'm whole-heartedly behind Brunel Line. It is easy to say, it honours someone worth honouring, it has the history wrt the route. And names like that do the job of distinguishing lines just as well as numbers and letters, if not more so as its more memorable than "OL1" or whatever.
@Si

I agree, Brunel & East London, plus Chingford, Enfield & Southbury are probably good names. Better than any of the Baker/Loo, Picc/Vic options. But to find a grand selection of names for the whole of London, if LO is extended, will just overburden the system. Imagine how many different lines would use Clapham Junction.

However, I don't agree that a prefixed route number is any less memorable than a name.. Who doesn't know a route 11 or 38 bus? So why not an OL1 or T6 or CX12 or whatever? Obviously, prefixes already used by bus routes should be avoided. Thats why a double prefix, perhaps with an L, is a good idea?
Who doesn't know bus routes? Lots of people!

Part of that is the nature of buses vs railways (easier to change where routes go, and far more of them with buses). Part of that is the non-geographic numbering system (OK, the letter prefixed routes) and that numbers are just labels and not the descriptions that names can be.

As a just-out-of-towner who has never really had to use London buses as the tube (which has never cost more than buses for me, given that I either have a travelcard, or travelled in on Oyster and will travel out and be very close to the daily cap anyway) or walking suffices for the journeys I make, I know very few. I do know the 38, having seen them around in various places along the route/heard people moaning about it in the transport geekery circles I take part in.

However, until I looked it up just now, all I could recall about the 11 was "Victoria?". I imagine that correct vague inkling puts me ahead of the curve when it comes to non-locals!

There's nothing wrong with numbers for navigation, just that names can be slightly better because they can describe the route. Names are also more aesthetically nice - not so sterile and can add something interesting. 'Brunel' is possibly the example par excellence for this.
I'm half and half on this between the Brunel line and the East London line - while many people remember its tube days and thus will never think of it as anything else, Brunel is short and easy to remember.

Am I the only one who is perfectly comfortable with Clapham Junction to Surrey Quays being known as the East London line? There's no need to cling onto the South London line handle, it wasn't a very good service anyway...
I get annoyed with SLL references in a way that I strangely don't wrt the WLL - perhaps because it is used for one branch and the other three are left as ELL (rather than the one branch each for NLL/WLL the latter having a shuttle as well), despite two of them going to South London.

You aren't alone the orange one - the SLL handle should be dead.
The East London and Atmospheric Railway
The Sellie might be in danger of getting known as the Silly










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