This question can be interpreted in two ways: what is the growth in rents on newly completed stock and what is the ongoing growth in rents on held stock?

Currently, there are two distinct sources of data, neither of which specifically answer the question for BTR.

The indices from Homelet, Zoopla and Rightmove measure the change in rent on lettings. However, these lettings are not confined to BTR stock.

The ONS experimental index of residential rents measures the growth in rents on occupied or newly let property.  Again, this is not confined to BTR stock.

The ONS have put together a useful comparison of the two series here describing the commercial indices as measuring flow and the ONS index as measuring stock:

The time series are short, but the average growth on new lettings of ~2.75% compares to the ONS figure of ~1.75%. Such data would support a hypothesis that the growth in rents on new stock runs at a little (maybe 1% pa) above inflation and that residential property rents depreciate by 1% pa.

Only time will tell and a bespoke index for BTR stock to answer the question specifically for this part of the market.