You may well be aware that the West Coast mainline is blocked at the moment, due to damage to the viaduct at Lamington, between Carstairs and Lockerbie.
Trains are running from Carlisle to London.
To get from Glasgow to Carlisle (or vice versa) you have two options
(a) A direct bus service
(b) A train via Kilmarnock and Dumfries, either the normal Scotrail service or the special shuttle service being run by Virgin Trains.
Due to the disruption to normal services, the restriction which says that Advance tickets must be used on the booked train has been lifted. However passengers are being advised to travel as close as possible to their original departure time.
As your outbound train is via Edinburgh to Kings Cross, this should run as normal.
The estimate to re-open the line is 31st January.
However in the case that it is not open by 5th February when you return, you can get a train from Euston to Carlisle and then either option (a) or (b) above. As your return train leaves Euston at 18:30, you should try to leave as close as possible to 18:30, but it doesn't have to be that exact train.
Regarding Euston to Tottenham Court Road, be aware that there are two branches of the Northern Line at Euston, the Bank branch and the Charing Cross branch. To get to Tottenham Court Road you need the Charing Cross branch.
As noted earlier there are also buses from opposite the station or a taxi would be about £10.