There's two parts to answering this question, one part being to note that there was still coerced labour, and the other part being to discuss why there wasn't more coerced labour.

What coerced labour was there in Britain in the 18th and 19th centuries

Britain did see coerced labour to some extent. For a start, there was coerced labour in the more dangerous jobs - think of Oliver Twist being sold to a chimny sweep, or girls being forced into prostitution (in a time of widespread syphillis and no antibiotics, this was very dangerous). In Scotland, a 1606 act had placed Scottish coal workers in basically slavery to their employer, and ruled that vagabonds could be forced into that compulsory labour. This was only ended by an act in 1799. Britain also, up until 1875, retained Master and Servant law gave employers the ability to criminally (as opposed to civilly) punish workers for breach of contract, and there were contracts of indentured servitude.

Why did Britain not see widespread coerced labour during the Industrial Revolution

I don't know any academic work that has been done specifically on this for Great Britain during the Industrial Revolution, but the classic article on the economics of slavery, and coerced labour (eg serfdom, indentured servitude) more generally was given by Evsey Domar, in 1969, (though Domar notes several authors, particularly Kliuchevsky, already had the idea). Domar's argument is that slavery only makes sense if it saves money over paying someone a wage. If you enslave someone and you want them to live more than a few months, you have to feed, house and shelter them, and you also have the costs of capturing them and stopping them from running away. Therefore slavery only makes economic sense if prevailing wages are substantially above subsistence cost - or the labour is highly dangerous or miserable (thus coal miners, chimney sweeps, prostitutes).

Domar used the example of the introduction of serfdom into Russia. To quote "before 1550 Russian peasants were free men; a hundred years later they were serfs". Domar relates this adoption of serfdom mainly to the Russian state's demand for more men for military service and the conquest of the steppes and thus their opening up to Russian farming. Therefore the demand for labour, relative to land, went up (Domar also notes a number of other factors, there's an ungated copy of his article linked below, I suggest reading it).

Domar also discusses Western Europe's serfdom, with the emergence of serfdom in the late Roman Empire and its decline by 1300. As the population of Western Europe grew towards the end of the 13th century, serfdom declined (though Domar puzzled over the failure of serfdom to be re-established after the population losses of the Black Death).

England in the 18th century was in a state where there was lots of labour available. England had an Agricultural Revolution between the mid 16th and late 19th century, and its last peacetime famine in the 1620s (arguably due not just to the improvement in agricultural production but also due to relatively effective enforcement of the poor laws), and there was a rapid growth in population alongside it, Maddison's long-term economic series estimates that British population went from 8.5m in 1700 to 21.2 million in 1820. There is plenty of evidence that GDP per capita also grew over this period, but this was not evenly distributed. There's a lively debate going on at the moment about how high British wages for labourers were over this period, but it certainly wasn't particularly high, not much above subsistence. A vivid example of low wages is actually a very old one - Adam Smith, in his The Wealth of Nations (1776) writes (in the context of what is a necessity and what is a luxury)

Custom, in the same manner, has rendered leather shoes a necessary of life in England. The poorest creditable person, of either sex, would be ashamed to appear in public without them. In Scotland, custom has rendered them a necessary of life to the lowest order of men; but not to the same order of women, who may, without any discredit, walk about barefooted. In France, they are necessaries neither to men nor to women; the lowest rank of both sexes appearing there publicly, without any discredit, sometimes in wooden shoes, and sometimes barefooted.

While obviously being able to afford wearing shoes during an English winter (let alone a Scottish one) is a valuable thing, it's not exactly a sign of high wages for free labour. 

There is other evidence for a lack of demand for coerced labour in England - the British authorities first sent convicts to North America and then resorted to colonising Australia to have somewhere to send criminals - they were willing to pay the costs of shipping people half way round the world by sailing ships rather than enslaving them at home.

So in England during the Industrial Revolution, a manufacturer didn't need to enslave people, they could hire them cheaply. 

Meanwhile, in the North American colonies, land was ample and labour was scarce, so slavery made economic sense as per Domar's argument.

Why wasn't there more coerced labour?

All this does raise the question of why Britain didn't reintroduce widespread coerced labour as wages rose during the 19th century, and why the northern US states abolished slavery. Laegerloff Nils-petter (2009) mentions the argument that perhaps industrial production is more care-intensive and the supervision costs of slavery got too high - think of stories of forced labourers under the Nazi regimes deliberately sabotaging artillery shells. Against this argument though there is evidence that slave societies used slaves in skilled positions.

Another possibility is that the inclusive social institutions needed to support industrialisation, such as relatively less-corrupt legal systems and protection of property rights, also bring about greater attention to the interests of workers in legal procedures, and protection of the property rights of the majority of the population (see Miomir and Milica, 2018 for a summary of the research). There is also some empirical evidence that people in more market integrated societies cooperate more and show more concern for their partner's well being in economic games (Henrich, 2001).  [Note I am aware that this argument about morality contradicts much academic literature which associates markets and capitalism with exploitation and selfishness. My understanding is that the key difference is the counter-factual, the work I'm drawing on compares what happened and happens empirically in industrialising economies to what happened and happens in other systems, as opposed to comparing what could be.]

It's noticeable that the abolitionist movement and the realisation of the horrors of slavery became widespread from the late 18th century in Britian, northwest Europe and northern USA. Sadly, the profitably of slavery in the southern states and the cognitive dissonance between the economic motive and the moral horrors may have driven much of the viciousness of US racism as slave owners sought to convince themselves against all evidence that their slaves were naturally subhuman. And it is important not to exaggerate the scale or spread of any change in values. This was far from universal, and often subject to human hypocrisy.

Or it could be due to some third factor that no one has thought of. There's a shortage of academic research into why not slavery.

In summary

Widespread slavery didn't happen in Britain at the start of the Industrial Revolution because labour was cheap and plentiful compared to the American colonies. That said there was coerced labour in particularly dangerous jobs. There is a puzzle that rising wages didn't lead to the reintroduction of coerced labour, this may be due to the changed nature of work or it may be due to cultural values charging to a more inclusive basis as part of the same processes that formed the institutional basis for the Industrial Revolution and subsequent economic development. 

Sources

Evsey Domar, 1969, The Causes of Slavery: A Hypothesis, Number 42 (https://dspace.mit.edu/bitstream/handle/1721.1/63299/causesofslaveryh00doma.pdf?sequence=1&origin=publication_detail)

Stephenson, Judy Z. 2019. Mistaken Wages: The Cost of Labour in the Early Modern English Economy, a Reply to Robert C. Allen. The Economic History Review 72 (2): 755–69. doi:10.1111/ehr.12780. (ungated working copy at http://www.lse.ac.uk/Economic-History/Assets/Documents/WorkingPapers/Economic-History/2016/wp231.pdf)

LAGERLÖF NILS-PETTER. 2009. Slavery and Other Property Rights Review of Economic Studies 76 (1): 319–42. doi:10.1111/j.1467-937X.2008.00511.x.https://mpra.ub.uni-muenchen.de/372/1/SlaveryOtherPropertyRights.pdf

Naidu, S. and Yuchtman, N. (2009) How Green Was My Valley? Coercive Contract Enforcement in 19th Century Industrial Britain,  http://www.eco.uc3m.es/temp/MS_paper_draft_june_2010_submission.pdf

Jakšić Miomir, and Jakšić Milica. 2018. Inclusive Institutions for Sustainable Economic Development. Journal of Central Banking Theory and Practice 7 (1): 5–16. doi:10.2478/jcbtp-2018-0001., https://content.sciendo.com/view/journals/jcbtp/7/1/article-p5.xml

Henrich J, Boyd R, Bowles S, Camerer C, et al. 2001. In search of homo economicus:  Behavioral experiments in 15 small-scale societies. American Economic Review 91:73-78