If you're car's not garaged I think you can get a solar panel trickle charger which sits on the dash board and plugs into the cigarette lighter outlet to trcle charge the battery. Try a google search.

Might get you over the problem?

Wouldn't the little red light on the dashboard come on if it was the alternator that was duff?

Fair enough but what car do you drive as I have never come across that being the case?

One of the items on the PDI list I have to go through on cars we sell is to check power outlet/cig lighter . There are lots that are live with the ignition off . Wasn't there supposed to have been something sorted about them being permanent live a few years ago ? IIRC it was after the newspapers went overboard about a couple of incidents involving children burning their fingers .
Which reminds me of a time when I was driving up the A1 with my lad . He kept passing sweets to me . I just kept accepting them and shoving them in my gob . Then he passed me the cig lighter .. OUCH

TBH I'm sure I've had cars in the past that had permanently live sockets in them, I had a Volvo V70 that had one in the boot because it came with a 12v cooler box plugged into it, a "gift" from the dealer that was probably added to the finance agreement - never used it once but the indicator light would stay on with the ignition switched off unless I unplugged it.

The Peugeot 307 SW (car from hell) that I had also had permanently live sockets in it because we spent 3 hours sitting on the dock of the bay in Roscoff waiting for a ferry one afternoon with the kids running the battery down watching videos in the seat-back thingys.