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Thanks for your suggestion, catsrcool. Things like this may be 'very easy to do' if you know what you're doing, but unfortunately I don't have a clue!
I have actually bought her a very bulky pink (!) Bush Bluetooth Boombox at a cost of £20. It needs 8 X C batteries to power it - £40 for rechargeable batteries, & a universal energiser charger £25. Not what I had in mind when I agreed with my daughter that I'd get it for the granddaughter's birthday. But she seems to be delighted with, which is what matters.
Many thanks to everyone for their attempts to steer me in the right direction. Having been round Argos, John Lewis, Maplin & several other smaller specialist stores, it appears that there is a demand for the sort of thing I was looking for, but requires too much battery power to fit into something the size of a fat tablet. Hard to understand when Ed's recommendation of a 9" portable DVD player has the requisite technology.