Being late to a train (UK) because of overground/underground cancellation?

The rules are not entirely clear.

Much as TFL likes to downplay it’s status, London Overground is part of national rail. The national rail conditions of travel explicitly allow use of multiple tickets for the same journey and the rules about taking the next train in the event of a missed connection due to disruption on a previous train apply to journeys.

What is not clear is if two rail tickets can be part of the same journey, even if there is a gap between them. It’s also not clear what happens if part of the journey is made by rail, but using a pay as you go scheme instead of a ticket.

The London Overground is part of the national rail network (here). According to the previous answer (“Through domestic or international tickets”), connections on the national rail network allow those on an advance ticket to continue on the next available train.
However, they also technically need to verify that you were actually on the delayed train (it is extremely unlikely that this would be enforced in practice). There is a section on all National Rail tickets for “Endorsements” (on the reverse side of the traditional orange ones)- where they stamp your ticket if you are subject to a delay. If you were following the absolute letter of the rules, you would’ve adressed the staff at Euston upon alighting for the magic stamp.

It is always worth asking the staff at the station if you can travel on a missed Advance ticket – around where I live a mumbled “I missed my bus” can usually get you on the next train.

This is covered in the Frequently Asked Questions about Advance fares section of the National Rail Enquiries (internal) Knowledgebase (iKB), which isn’t available online officially. However, one of the nice members of Rail UK Forums posted that to their site earlier in response to a different query. The relevant question in the FAQ is this:

Q22 – Can a passenger travel on any trains other than the one on which they are reserved, without changing the booking?

A: The following principles apply.

1). Start of the Journey. It is the passenger’s responsibility to turn up at the start of the journey in time for the first train. If they miss it due to problems parking, taxi not turning up etc, they must buy a new ticket;

2). Once the journey has begun. If the passenger is delayed and the rail industry or its partners (as shown below) is at fault, which should be checked with your Control Office, change to another train of the same company is allowed to get them to their destination with the least delay. This is irrespective of combinations of rail tickets held. Examples are:

Included: are passengers travelling on valid:

• Through domestic or international tickets; e.g. Brighton – Scarborough route “+TOC X & Connections”;
• Through rail & partner tickets for which there is a through bus, tube, ferry or metro fare, e.g. Zone U12 – Leeds, Wisbech Coach – York; Ryde Pier – Hull, etc;
• Combination of domestic rail-only tickets
  e.g. rail season ticket Skipton-Leeds plus Advance ticket Leeds-Peterborough; or adjoining Advance tickets;
• Combination of domestic rail & partner tickets
  e.g. Brighton – Zone U12 plus Advance ticket London-Manchester, or
  e.g. Advance ticket Bristol-Paddington plus tube single ticket plus Advance ticket Kings Cross to Hull.
• All-Zones Travelcard, PTE-products etc (where rail is included) plus Advance ticket;
• Combination of Eurostar tickets into the UK and then either advance purchase tickets from London Terminals or “London Intnl CIV” or “Lndon Eurostar CIV”.

Not included: for the avoidance of doubt, are:

• Non train-company travel on separate tickets e.g. journeys that commence on bus-only, tube-only, ferry-only or metro-only tickets. (This includes “PlusBus” which is a local day- Rover bus ticket, not compatible with a medium/ long distance ‘Advance’ single journey, so are kept as separate tickets);
• Tickets that cannot be read on-train e.g. smartcards (but allowable where electronically checked, delay verified and Advance ticket endorsed in Travel Centres).

So, because you had left enough time for the trip, and because the delay was the fault of the railways, you would be able to get your ticket changed/endorsed for free onto another later service from the same company.

However, if you’d missed the train due to a delayed bus, or a delayed taxi, or traffic on the roads or similar, then you’d have to buy a new ticket at your own expense (unless your travel insurance happened to cover it!)