London to Cambridge

The name of the Station you are arriving at is Euston (pronounced yewston).

There are three London main line stations that will get you to Cambridge in about one hour - Liverpool Street, Euston (take tube to Finsbury Park and change to train) or Kings Cross. Fares vary but a single from Liverpool street is around six pounds and increases. Euston is the most expensive option. National Express (bus takes about two hours and costs 15 Pounds).

Have a look at thetrainline.com - gives you information on trains, times and fares. Trains to Bath involve returning to London taking either taxi or tube with two changes. Would look at the National Express coach website - about the same time, but cheaper and only 1 change at Heathrow airport.

I would have done it this way. Not taken the night train but left Edinburgh on a morning train. You could easily then have reached Cambridge without going anywhere near London by making one simple change at Peterborough. So, the journey would be Dep EDB at 9.30am > arr. PBO at 13.07 (change) Dep. PBO 13.18 > arr.CBG 14.08. (It is probably cheaper to split the tickets - possibly at Peterborough).

You could also have gone direct from Edinburgh or Glasgow to Bath by train with 1 change at Bristol & possibly Birmingham. This would be more convenient that bothering going into London. Again, split ticketing would probably give the cheapest fares - along with advance booking.

www.nationalrail.co.uk
http://www.moneysavingexpert.com/split-cheap-train-tickets/
www.eastcoast.co.uk
www.virgintrains.co.uk
www.crosscountrytrains.co.uk

"Have a look at thetrainline.com"

The Trainline charge a booking fee, book tickets with the train operating companies.

The Cambridge-to-Bath trip will go back through London, and you also connect by Tube or taxi from London Kings Cross to London Paddington station. (National Express buses on this route are less frequent , slower, and also include a connection, usually at London Victoria station).