There was Scottish influence and participation throughout the First British Empire, which makes calling it an English endeavor more than a little misleading. Another poster has mentioned the spread of Scottish settlement across the Atlantic colonies, so I won't go into that, other than to mention Ned Landsman's excellent Scotland and Its First American Colony, 1683-1765, which is about East Jersey and the massive influence Scottish settlers had on it socially, politically, and culturally.

So, for my main points, let's first consider the role of Scottish merchants in furthering transatlantic commerce. Even before the Act of Union, they were semi-legally involved in carrying American produce eastwards across the Atlantic and carrying European goods westwards. Caribbean sugar especially was a real hit in Scotland. After the Act of Union, that activity exploded, centered on Glasgow initially but expanding to other Scottish ports in later decades. This is actually one of the reasons why Bristol, Liverpool, and London merchants were more than a little suspicious of the Union, since the Scots could now trade with the colonies on an equal footing with English merchants.

Next up is the role of Scottish colonial administrators. Two that spring to mind from my own work are Archibald Hamilton, governor of Jamaica 1711-1716, and Robert Hunter, governor of New York 1710-1719 and governor of Jamaica 1727/8-1734. Both were influential in their own ways--Hamilton was a failure who poisoned the Jamaicans against the crown for a decade, while Hunter was a deft politician who won settlements of crown revenue in New York in 1714-5 and in Jamaica in 1729. Hunter also brought a number of young ambitious Scotsmen with him who influenced New York society and politics for a generation after him, especially Cadwallader Colden, who played a major role in the Zenger libel trial (see Ned Landsman's From Colonials to Provincials: American Thought and Culture, 1680-1760). Below the gubernatorial level, there were substantial numbers of secretaries and militia officers, even before the act of Union (English-descended Jamaicans had quite the moan about this in the 1690s and early 1700s).

That leads me nicely to my last point. Scottish soldiers and sailors played an important role in defending and expanding the Atlantic empire throughout its existence. The most well-known instance of this is the Battle of the Plains of Abraham in 1759, in which Fraser's Highlanders took more casualties than any other British regiment on the field. But again, even before the act of Union there were Scots serving in military capacities in the colonies. From my own work again, I know that they were one of the mainstays of the Jamaican militia as early as the 1690s. There has also been a suggestion that the Caribbean sugar plantations especially were reliant on Scottish overseers who had military experience but no other real prospects for employment. You could look into more on that in Peter Linebaugh and Marcus Rediker's The Many-Headed Hydra: Sailors, Slaves, Commoners, and the Hidden History of the Revolutionary Atlantic.

I haven't touched at all on the role of Protestants born in Ireland who settled or worked in the colonies, because that opens up a whole can of worms about Englishness, Irishness, and Britishness that I have no desire to touch in a reddit comment. Let's just say that people throughout the British Caribbean were complaining about "Irish lawyers" from the 1690s onwards, which indicates that they were there and exerting influence. Two of the most prominent were Hugh Totterdell in Jamaica around 1695-1714, and Gelasius MacMahon in Barbados in the 1720s and 30s. Totterdell was probably a republican, and MacMahon wasn't far from it--and both of them played major roles in frustrating the crown's centralizing efforts in those colonies.

All of which is to say that calling the First British Empire an English Empire would ignore the major contributions of Scottish people to the functioning of that empire at all levels, and probably marginalize the Irish even more.

[EDIT] Apologies for the low-quality post, here is a more comprehensive answer to your question.

To address whether the First Britsh Empire was predominantly made up of Englishmen, we must shed light on the domestic situation in Britain and Ireland before the British Colonisation of the United States.

Throughout the 11th and 12th centuries, the Normans had been attempting a series of conquests in Wales and Ireland looking to expand their territory which started mainly with King William I, also known as William the Conquerer. William established several Earlodoms in Welsh land as early as 1080. Through a series of military campaigns, Wales fell under English rule, though much of the Gaelic princes retained some power and united under Prince Llewelyn Fawr to regain some of their lands whilst the Normans where feuding following the death of King Henry I (William I's Son). The Welsh took this as an opportunity to recapture some of their lands and also claim Norman land for themselves. An uneasy peace lasted between the two kingdoms up until when Edward I became King of England in 1272 following his father Henry III's death. Edward had a disliking for the Gaels and in 1277 launched a large scale military campaign into Wales which quickly overwhelmed the Welsh forces, resulting in Wales virtually becoming an English colony by 1283.

The Norman Invasion of Ireland started in the Late 12th century when deposed King of Leinster Diarmaid Mac Murchadha invited a Norman host to Ireland in order to help him reclaim the throne taken from him by the High King of Ireland Ruaidri Ua Conchobair in 1167. Ireland was divided into several Kingdoms at this time, united under a High King. Ireland's main port towns such as Dublin, Waterford, and Wexford were ruled by the Norse-Gaelic who were the assimilated offspring of the Viking settlers.

A host of Norman mercenaries landed in Ireland in 1169 followed by two more landings in 1170. Led by the Earl of Pembroke Richard "Strongbow" de Clare. The invasion resulted in the Norman control of Leinster and the Norse controlled port towns. The Gaelic Irish retained control over the rest of the country through the Treaty of Windsor in which Henry II gave control of the rest of Ireland to High King Conchobair, however this quickly dissolved and Henry adopted a new policy and made Ireland a Lordship and bestowed the title on his son John. The areas surrounding Dublin and most of Leinster remained in Norman control but the rest of the country quickly fell back under Gaelic control. Throughout the next 500 years, Norman control would dwindle to the small area surrounding Dublin and the Wicklow Mountains, which would become known as "The Pale". This area was settled with Normans and developed into an English controlled province defended from the Irish clans who controlled the rest of the island.

Despite numerous attempts at an English invasion of Scotland during the 13th and 14th Centuries, Scotland and England remained independent countries in their own right, each possessing its own parliament and monarchy. This changed in 1603 when King James IV of Scotland also inherited the English throne after the death of Elizabeth I who became Queen of England in 1558 and did not marry or have children. James, now James I of England worked on reconciling the two Kingdoms as they were now both under a protestant King. Although retaining independent parliaments for some time, after a series of civil wars, the parliaments were united into the Commonwealth of England, Scotland and Ireland in 1657, although Ireland remained mainly in the control of several Gaelic clans.

By the time of the formation of the East India Company in the early 1600s and the rise of British colonialism from the 1650s onwards, Britain was, in essence, a unified colonial empire, although most of Ireland remained under the control of the Gaelic clans. The expansion of the British Empire into Africa and the Americas where a joint effort by all peoples of Great Britain, however, a considerable number of people in Wales and Scotland would retain nationalist ideologies.

I hope this helps!