One off Facel Vega... I say so because of the wheels and because it just looks "French"..
Not Facel Vega and not French. Wheels are of the same brand fitted to many a Facel Vega, yet they were in no way exclusive to that car and were not French in origin.
Doesn't ring a bell yet. I first looked at Gilbern and today was trying to learn more about Peerless/Warwick prototypes but couldn't find anything with Tatra-like rear window.
Original bodywork by Panelcraft. Later scrapped when the car was turned into an open DB3S in the 1990s....
I'll give someone else a chance to solve, but here's another pic to make it easier : Image Unavailable, Please Login
Damn, I knew the flank looked Astony, but the tail reminded me of a '+' something. Good find. Now on to the Fiat Packard
Okay, I stepped in it and likely ruined it for everyone, so I'll just go ahead and solve: Moretti coupe based on Fiat 1500 chassis. Here's the next one: Image Unavailable, Please Login
That's right Wayne; it's a Moretti coupe, but this one is presumably based on a 2100 Fiat (your pic is of a 1500 though...). Almost identical as far as I can tell.
I've seen both chassis - 1500 and 2100 - attributed to this little car, but I believe that 1500 is correct. For comparison, here's an image of the very similar (but larger) coupe by Moretti based on the 2100 chassis: Image Unavailable, Please Login Image Unavailable, Please Login
Ah, I see you edited this post and I think you're correct. The museum car does look like it's the 2100 chassis car.