This historiography for this question is long and multifaceted so I'll keep it short. JR Seeley, a British historian in the 1880's said that the British seemed to obtain their Empire in a 'fit of absence of mind' and since then British imperial and later cultural Empire historians have been looking to answer this question- for a general read on this topic see Phiippa Levine's The British Empire: From Sunrise to Sunset.

There are quite different answers depending on the time frame and what historical approach you want to take. Generally speaking there was quite a bit of awareness of British imperialism early on with people like Edmund Burke and other "conservatives" rallying against it. In the arena of high politics imperial endeavours in the 18th century were generally undertaken by private companies like the British East India Company, which was harshly criticized by leading British thinkers. There were other aspects of Empire, like the system of racialized slavery, in which more "common" people were well aware of and formed boycotts against items obtained by slave labour, like sugar. In fact enslaved peoples like Mary Prince, and others would visit Britain and travel around making public speeches about the evils of slavery. There were also the so called "settler-colonies" like Canada, the US, Australia, New Zealand, and South Africa where landholding elites would encourage settlers to live, but this was small scale up until the 1830s, and, importantly becoming a settler was quite looked down on. There are also examples of Indigenous peoples from what eventually became Canada, like Peter Jones, who also travelled to Britain and took audience with the queen in the 1830s. These are just a few examples of what Britons knew of Empire.

As the 19th century progressed and major events like the Indian resistance of 1857-8 saw the transfer of power of the governance of India to the British Crown and away from the British East India Company. This meant more British state directed imperial endeavours, and consequently, "celebrations" of Empire, like the 1851 Great Exhibition. From the mid- 19th century onwards Britain experienced a great political change with the ascendancy of liberalism, where Empire was praised, and where the British government made efforts to regulate settlers flooding into the 'settler-colonies' this is where large scale settler migration happened, and the narrative about becoming a settler changed. Migration went both ways, and there was quite a bit of presence from peoples from "non-settler" colonies like India living and working in Britain.

By the late 19th century Empire was seen generally positively and advertisements for products like pears soap began using Empire imagery in their ads, using tropes of darkness/ uncleanliness/ colonized peoples contrasted with whiteness/ cleanliness/ British peoples. I could go on, but I would argue that Britons knew quite a bit about Empire, from boycotts, from colonized peoples living in Britain, to cultural iconography using images from the Empire in advertisement.

Edit: Britons knew of Empire, some harshly criticized it, those who justified it usually did so under a liberal worldview, take JS Mill for example who said Indians and others had to be governed because they were child like, and had not reached the appropriate stage of civilization that he thought Britain had. TR Metcalf's Ideologies of the Raj is an excellent work on this topic that explains how Empire was legitimized by liberalism and liberal thinkers