Just as a "by the way" since the title mentions musicians in UK museums, (and I know it has nothing to do with the EFDSS project above), it is a relatively common occurrence to see musicians in the National Museum of Scotland in Edinburgh: during Edinburgh Festival, there are often lunchtime concerts in the ground floor area of the newer extension.
At other times there are themed "lates" in the big hall in the older part of the building. There is to be one of these on the evening of Friday 10th November, just towards the end of the exhibition re Bonnie Prince Charlie and the Jacobites, which has been running for the last few months, with a ceilidh band called...."The Jacobites" playing for dancing.
The Mining Museum at Newtongrange also has musical events from time to time, often featuring songs about mining.
And there will be others around Scotland.