There were some HALEs at Selborne but the Revd COBBOLD was a very uncompromising man, very much loathed by the majority of his poor parishioners, who suffered very low wages due to excessive tithes levied on the farmers for whom the ag labs worked.
Unfortunately, it appears that the earliest available Board of Guardians' Minute Book for the Alton Union dates from the mid-1840s. However, there are some general accounts that might reveal the parochial history of Poor Relief 1820s - 1840s. I think Nell is right: the starting point is the marriage cert for Lucy.
One aspect that did strike me: COBBOLD was killed in an accident in London in the 1840s. If the presence of the certificates with the deeds for the Oakhanger cottage sale c1851 is an indication of possible litigation, Lucy's share - if any - from the proceeds of the sale would have stirred an interest from the Guardians to recoup their expenditure on relieving her and her family.
If you'd like to learn a bit about the local social history during the Swing Riots, take a look at Peter Higginbotham's website and enter Selborne in the search box:
http://users.ox.ac.uk/~peter/workhouse/