That depends on what the grant is for. If it falls under one of the statutes that permit a local council to spend money, there is no limit. Although the electorate will be up in arms if the spending is unreasonable and a council can't spend more than it has (except by borrowing, which requires permission).
For example, local councils have a statutory power to make grants for the upkeep of a churchyard, and this does not have a specific limit.
Where no statute is relevant, the council can use "Section 137" (of the 1972 Local Government Act) to do pretty much anything that can be shown to provide a commensurate benefit to the local electorate. In this case, there is a limit on the total spending per year under Section 137 across all such grants. It's determined by a formula. For the financial year 2011-2012 the limit was £6.15 times the number of electors.