If I purchase a property with ground rent can this keep going up indefinitely?

The Lease will set out how the rent increases if at all. Some older Leases provide for a fixed rent throughout the term of the Lease. Newer leases sometimes provide that the rent increases at intervals of, say, 25 years, to a fixed higher amount until the term comes to an end. Other leases stipulate that the rent payable for an intial period of, say, 25 years is a fixed amount following which the rent changes to an amount assessed by a fixed formula, often by reference to the Retail Price Index.

The ground rent payable under a Lease continues throughout its term unless the leaseholder extends his Lease under rights given to the tenant by statute, the Leasehold Reform Aft 1993, in which case the ground rent changes to a peppercorn rent. A peppercorn rent effectively means no rent at all.