I have a Roku Express 4K. I am in a dialogue with the iPlayer support people over an inability to start iPlayer - the splash screen shows up, goes away for a moment, then comes back and just sits there - but have also seen the buffering on many occasions.
Only iPlayer is affected, not (for example) Netflix and ITV3. I have tried every measure up to and including factory resets on multiple occasions.
A recent clue to what is going on may be the following.
I have had a broadband outage that turned out to be an iffy cable incoming to the property. The (excellent) Virgin technician not only fixed that but discovered an unnecessary attenuator in the connection to the hub. Once that was removed the broadband speeds, which had always been very satisfactory (tens of Mb/s, though reported by the Roku device as merely being "good" at 7-10 Mb/s) increased noticeably - a factor of two or so. The important observation is that my connection problems with iPlayer went away immediately.
My conjecture is that the software in the Roku device and iPlayer respectively have an incompatability, perhaps a timeout set to too low a value. Either the Roku is giving up too soon when expecting a communication from iPlayer, or the reverse. The fact that Netflix and ITV3 work perfectly makes me think that the bug is more likely to be in the iPlayer software, but this is not necessarily the case.