The airlines cancelled the flight because of Storm Emma, do I have the right to ask them to pay for the train and the hotel?

Under EU261, meteorological conditions incompatible with the operation of a flight is one of the exceptions given to the regulation, so in your case its a very mixed bag.

While there exists an exceptional condition, that does not necessarily absolve the airline from the Right to Care, so you may have a case for the provision of a hotel:

Article 9

Right to care

1. Where reference is made to this Article, passengers shall be offered free of charge:

(a) meals and refreshments in a reasonable relation to the waiting time;

(b) hotel accommodation in cases

• where a stay of one or more nights becomes necessary, or

• where a stay additional to that intended by the passenger becomes necessary;

(c) transport between the airport and place of accommodation (hotel or other).

2. In addition, passengers shall be offered free of charge two telephone calls, telex or fax messages, or e-mails.

3. In applying this Article, the operating air carrier shall pay particular attention to the needs of persons with reduced mobility and any persons accompanying them, as well as to the needs of unaccompanied children.

However, this is certainly only intended for a provision of care while you are in transit with the airline - if you choose a re-route to London instead of Glasgow, then the airline would almost certainly be within their right to consider their duty to you complete, and you would no longer be in transit with them and thus no longer entitled to a hotel or other provision.

With regard to the re-routing via train, you will almost certainly fail in this regard, as the regulation only talks about an obligation to provide re-routing via another airline, not another method of travel (specifically "under comparable transport conditions").

Article 8

Right to reimbursement or re-routing

1. Where reference is made to this Article, passengers shall be offered the choice between:

(a) - reimbursement within seven days, by the means provided for in Article 7(3), of the full cost of the ticket at the price at which it was bought, for the part or parts of the journey not made, and for the part or parts already made if the flight is no longer serving any purpose in relation to the passenger's original travel plan, together with, when relevant,

• a return flight to the first point of departure, at the earliest opportunity;

(b) re-routing, under comparable transport conditions, to their final destination at the earliest opportunity; or

(c) re-routing, under comparable transport conditions, to their final destination at a later date at the passenger's convenience, subject to availability of seats.

The only exception to this is if the airline can get you to another airport that serves the same destination, in which case they are obligated to transport you to the original destination or to another agreed destination close by.

3. When, in the case where a town, city or region is served by several airports, an operating air carrier offers a passenger a flight to an airport alternative to that for which the booking was made, the operating air carrier shall bear the cost of transferring the passenger from that alternative airport either to that for which the booking was made, or to another close-by destination agreed with the passenger.

London to Glasgow would not be considered "close by".