You can take a train from Northampton to Colchester via Milton Keynes Central, Euston Underground Station, King's Cross St. Pancras Underground Station, and London Liverpool Street in around 2 h 25 min. Alternatively, National Express operates a bus from Northampton to Colchester once daily. Tickets cost $14 - $19 and the journey takes 3 h 55 min.
From Northampton train to Milton Keynes Central, train to Euston Underground Station, Tube to King's Cross St. Pancras Underground Station, Tube to London Liverpool Street, then train to Colchester. 2 h 25 min £62. From Northampton bus to Colchester. 3 h 55 min £13. From Northampton drive to Colchester. 1 h 56 min £19.