London, Euston and London, Victoria both have underground stations on the Victoria Line.
The journey time is about 8 minutes.
Take a Southeastern Train from Greenwich to London Bridge and then the Northern Line to Euston The journey time is around 40 minutes.
10 minutes
About 25 minutes by cab.
About 1 hour
About 1 hour 30 minutes from Waterloo Station.
About 20
As there are no direct trains from Heathrow to London Waterloo, it's quicker to travel by underground from Heathrow on the Piccadilly Line to Leicester Square Underground Station and then change onto the Northern Line to London Waterloo Railway Station.
About 35 minutes.
50 minutes
It depends entirely on traffic conditions but allow about 30 minutes.
About 4h15 by changing at Banbury and Princes Risborough. About 4h05 by changing at London Euston and London Marylebone.
About 2 hours - but it depends on traffic conditions at the time.
Trains don't go from Kings Cross to Manchester. They leave from London Euston which is a 10 minute walk from Kings Cross. The journey from London Euston to Manchester Piccadilly takes around 2 hours 10 minutes.
4 hours and 30-50 minutes. This requires a short trip on the London Underground between Euston and Victoria or Waterloo stations. I'd also look to see if there's a feasible Manchester - Southampton service (change at S'hampton for the short journey to Portsmouth.