As luck would have it, and as I needed to go for milk anyway, I took a look in the local charity shops, and they had a new, apparently unused French Press on the shelf, so I bought it - at just £2.49, it would have been rude not to. I am just having my second cup of coffee from it. Yes, it does taste very different to that of my electric drip machine, but I'm not sure quite how different, not stronger, perhaps more flavours and slightly less bitter, more sophisticated, especially the second cup. It seemed to keep the second-cup acceptably hot, hotter than the machine, so that may not be problem.
I use the same make of coffee, as Mottie, from Lidl - Bellarom except the ready ground, vacuum packed version.
I almost never buy coffee whilst out, from the fancy coffee shops, I much prefer my own. The worst possible option whilst out and about, is the filter coffee some sell, where it has been kept warm too long and has turned bitter.