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Got to be honest, I didn't realise it wasn't in HD, but in case you missed it, BT announced that the app would now provide HD streams from January.
More details here: High Definition (HD) on the BT Sport App and online player
I've just checked my iPhone and the app does indeed give me some new viewing options when using the enhanced player:
BT Sport App
I cannot at this time find any information on any changes to the stream quality when using a Chromecast, so I assume this is still "up to 720p".