( for context started as comment after C Mackinnons reply but got too long!)
The repeal of the Corn Laws may certainly have led to the migration of tenant farmers and also labourers . There's an increase in some parishes in the 1860s onwards. Many smaller farmers found themselves in an increasingly dire predicament .Cheaper imports resulted in the decline in profitability for arable farming.
Here's a couple of papers discussing it.
Irish emigration and Corn law
Farmers and Emigration
However, Sandhurst emigrants to NSW were encouraged and paid for by the parish far earlier in the century under the provisions of the New Poor Law, 1834 and this wasn't the earliest that poor people had been assisted to emigrate by this parish.
Unemployment after the Napoleonic wars as mentioned above, was high. ( a cause of the introduction of the corn laws. This certainly led to increased bread costs and in urban areas led to bread riots and discontent but England was still largely rural.Increased unemployment and in particular seasonal rural unemployment led to demands from the able-bodied for poor relief. The introduction of farm machinery further decreased the need for labourers. A succession of poor harvests added to the misery. At the same time family size also increased.
Under the Poor laws, the ratepayers of a parish were responsible for providing relief. In some areas local magistrates enforced the payment of relief in the form of wage subsidies ( for example, for each child over the third, scales dependent were used in some places). Costs to the rate payers increased and various methods were found to reduce costs. Mostly these involved make work schemes, able-bodied, unemployed men in need of relief were directed to work on the parish roads, quarry stones for building or instructed to work for each farmer in turn (roundsman system)
Payment for emigration expenses from the parish rates, was a possible method to reduce costs.It was an attractive option to many of the poor themselves, faced with a lifetime of low wages, frequent unemployment and poverty. It was attractive to the parish in that It reduced the number of potential paupers. However, though it could save money in the long run, it would add a hefty cost to a single years rates which were calculated on an annual basis. Magistrates in some places would refuse to allow the cost to the poor rate for 'grey areas' like emigration costs. A single rate payer could also challenge the cost which could result in the overseers of the poor having to reimburse the money. Nevertheless, some parishes did work out the means to pay emigrant's costs. In 'your parish of Sandhurst, a number of people, in the 1820s. had their passages to the US paid for by the parish. The parish raised the funds from loans provided by wealthy parishioners. https://www.kentarchaeology.org.uk/Research/Pub/ArchCant/Vol.073%20-%201959/Misc/235.htm
The increasing costs of poor relief in Southern England and the Swing riots (which of course started in Kent) led ultimately to the reform of the poor laws. The New Poor law meant that the able unemployed were to be relieved in workhouses, rather than out relief 'at home'. If the concept of emigration was attractive to many before the act, it was more attractive after it. The poor law commission also enabled parishes to the assist emigration of able-bodied workers. http://www.workhouses.org.uk/emigration/ Your parish, by then part of the Cranbrook Union but still responsible for it's share of the costs, took advantage of this scheme, with £80 being paid for emigration by 1839.
6th Report Poor Law Commisioners, google books (unfortunately no numbers of emigrants, given.It's possible you might find these in later reports)
Given that wealthier ratepayers in Sandhurst seem to have provided the finance for the 1822 emigrants to the US, it might well be that this wasn't just a 'shovelling out the poor' which is one way that pauper emigration is categorised but a stems from a more 'paternalistic tradition' which suggests a more benign motivation.