Driving in London is not for the faint-hearted. It's not as bad as Paris or Rome, but I'm going by my experience as a pedestrian in the last two. I drove in London for three years, but I knew my way around reasonably well - in that if I went the wrong way I could identify roughly where I was and that if I followed signs to the Elephant & Castle I could get back to Waterloo, or that I could follow signs for Woolwich to get back on the right road for Greenwich.
Driving in England is probably more of a culture shock for Americans than vice versa. Many Brits pick up cars in America and drive to their villas/ hotels, especially in places like Florida. But we're used to driving manual, so automatic is a breeze. You have much wider roads and you don't have all the quirks we do. For example zebra crossings, pelican crossings and toucan crossings. And roundabouts.
Driving in mainland Europe would feel more comfortable of course. But you'd be best in a left hand drive car. Again, many friends and family have rented cars abroad and had no trouble with the roads and traffic systems.
Don't take a car to Amsterdam though!
Still, if you'd only be there for a day you could just park up on the outskirts anyway.
I like your expansive dreams.
You know you'd never stick to the schedule anyway. Start off in the 'Dam. Find a good coffeeshop, find a trans* bar and go home eventually realising you didn't even take any photos. Or at least none in focus
