The following is a compilation from different sources, including the New England Historical and Genealogical Register, Grant Family website, and various encyclopedias on the internet. Verify by "Googling": "Battle of Dunbar", "Battle of Worchester", "Oliver Cromwell and the Scottish", "Cromwell and the Stuarts", and "Commander David Leslie of the Scots", to name but a few.
These facts are taken from "Scottish Battle" by C. Stewart Black, publlished by Brown Son & Ferguson, Ltd; Wikipedia:
The Presbyterians of Lowland Scotland had the strongest objection to King Charles I as a religious dictator because of his Catholic sympathies. But, they were entirely loyal to the House of Stuarts. So, when Oliver Cromwell captured Charles I and had him executed for high treason, the Scots openly defied Cromwell. They crowned Charles II King of Great Britain, France and Ireland on Jan. 1, 1651 in Scotland. (At this time Cromwell had declared himself ruler of the Commonwealth of England. He had considered crowning himself, after the execution of Charles I.)
Cromwell was furious with the Scots' defiance. He crossed the Scottish border with 16,000 men and marched to Edinburgh. The Scots had organized an army lead by the competent and experienced Scottish General, David Leslie.
Unfortunately for Leslie, his army was controlled by a Scottish parlimentary committee composed largely of ministers and clerics. These godly men had little military experience, but didn't hesitate to over-rule Leslie's experienced judgement whenever they saw fit. Even so, Leslie met Cromwell and his men between Leith and Edinburgh with 26,000 Scottish soldiers. His soldiers had been put under severe scrutiny by the parlimentary committee which determined that each man be "strong in the word" as he was with the sword. Some 4,000 men were expelled from Leslie's army for lack of Godliness. These expelled men were probably the most experienced fighters. Leslie was left with the clerics' and ministers' sons.
Yet, Leslie drove back Cromwell's forces to the harbor at Musselburgh. This harbor was not a good base and prevented Cromwell from getting supplies. In one month, Cromwell lost 5,000 men due mostly to disease brought on by exposure and insufficient food.
Cromell was forced to move south. He fell back on Dunbar. On the same day, Leslie's troops took command of Doon Hill which overlooked Cromwell's forces. Cromwell admitted it would take a miracle if his troops got out of this trap.
The next day, the Scottish committee told Leslie to attack. They saw victory in their grasp and they wanted it, now. Nothing Leslie said could persuade them to wait. Some of the preachers began to lead their companies down the hill. Leslie had to follow.
The English couldn't believe their eyes, and their luck! Cromwell and his men defeated the Scots. At Dunbar, 4,000 Scots were killed and 10,000 were taken prisoner."
Some of the officers were sent to Virginia as indentured servants. About a 150 were sent to New England on the ship "Unity" to work in a couple of ironworks. Peter Grant is listed as working at the Lynn ironworks. Also, in Kittery, ME, there is a Unity Parish which served prisoners who worked at the sawmills. Peter is included in this list, too. A few years later another small group was brought to a place in Maine called Scotland. James Grant, possibly Peter's brother, was in that group. After the Battle of Worcester, Cromwell sent more prisoners to New England in the ship "John and Sarah", John Green, master. The spelling of the names is challenging but there were several Grants listed as "Graunt". Alester, Alexander, Daniel, James, a 2nd James, a 3rd James, 3 Johns, Patrick, Thomas, and William; from "A List of Scots prisoners sent to New England around 1651" by Janice Farnsworth, internet.
On January 6, 1657, Peter and James were among those who formed the Scots' Charitable Society for the relief of Scottish prisoners in the New World. In 1661, Peter and James were ordered by a local court in Kittery, to return to their wives in Scotland which they did not, being exiled, or for other reasons.