Is our ground rent price increase determined by the RPI or the cost of living index ?

There is no such thing as a "Cost of living index". The RPI (Retail price index) is the most common but not exclusive measure and is calculated each month by taking a basket of commodities i.e. bread, milk, fuel...and analysing the typical cost to households each month and year. Therefore if your ground rent was set against this measure it would seem logical, howver it is unlikely. The RPI does not take into account mortgage interest rates and therefore makes the RPI an untrue picture of the actual cost of living as it makes no allowance for what the homeowner/landowner may be paying out of their pockets. Therefore it is more likely that any ground rent you pay will be increased in line with the land owners increase in costs which may well include mortgage payments and as such will probably not follow the RPI. Hope that helps.

My ground rent was set at the start of my lease to increase every 25 years.

You need to look at your conrtact. They could do it this way or a set annual percentage.

Look at your lease - that should tell you. If it is a VERY old lease, there may be something called a 'side letter' appended to it which will cover increases.