International first (and business) class for long flights is a very different product than most domestic first class services.

For example, here's first class on a United domestic 737: Wikimedia Commons: LuccaV

Here's "business class" on short-haul Lufthansa (simply an economy seat with the seat next to you blocked off to give you more room) Flickr: travelingotter

Here's international GlobalFirst on a United 747: Wikimedia Commons: Altair78

And here's a first class suite on Emirates: Flickr: omeyamapyonta

As you can see, the comfort and service are quite different. US domestic first class generally gives you a wider seat, a bit more legroom, no middle seats, free drinks, and snack and/or meal. (One significant exception being SFO/LAX-JFK/EWR routes, which some airlines operate as a much nicer flagship service.) These are all fine things, but how much are you really going to pay for them on a flight lasting a few hours?

In contrast, international first class is a much nicer experience. Amenities often include lie flat seats, bedding and duvets, fine foods like expensive champagnes and caviar, access to quality airport lounges, and even sometimes extras like pajamas, an on-board shower and bar/lounge (Emirates A380), and complimentary spa services at the airport lounge.

As a comparison, United's domestic first seats offer 37-39" of legroom and a 20.5" width. United's GlobalFirst service (where it's still offered) offers 78" flat beds and a 22" width. At the most basic level, international first class takes up considerably more space on the plane.

Now, in the case of your specific flight, there's an important clue in your screenshot: the word "refundable" under first class. While you might be buying a ticket in economy, business, or first classes, there are over a dozen "fare classes" that you're really buying. A super discounted economy ticket may be sold in O class, while the most expensive first class tickets will be sold in F class. They all offer the same service on the plane, but the fare rules, especially around changes and refunds, will vary, and airlines will manage the supply of seats in various fare classes to maximize their profitability.

You're booking this particular flight at the last minute, it leaves in four hours. That's unusual, and outside of a special last-minute fare sale offer, generally indicates a strong need to get to London immediately, perhaps for an important business meeting. The airline, based on its experience and knowledge of the market, how full the flight is, and other secret pricing strategies, believes it has at least some shot of getting someone to pay a $19,500 for a first class seat. Why? Because some people for whom money is no object do show up at the last minute wanting to fly first class. If one comes along, the airline will happily sell it at that price. If not, they can try to sell an upgrade to someone else who already has a ticket for cash or miles, or even let the seat fly empty. Either way, they're only willing to sell F-class fully refundable first class fares for this flight right now, and you will pay through the nose if you must have one.

In your comments, you seem to indicate that there should be some kind of fixed ratio between economy and first class pricing, but that's not how it works. The airline adjusts prices to try to maximize their revenue. While the supply and demand curves for first class and economy class seats are related to each other (funny things start to happen if all you have left is full-fare economy and discounted first, and that does happen occasionally), they are still separate products and are priced separately.

All of this may change for flights booked farther out in the future. Airlines can and do offer discounted first and business fares, usually targeting leisure travelers. These fares generally aren't fully refundable, but they might cost a fraction of that price.