The interbank market, as the name implies, is where banks trade currency, and it is frequently built on trades worth millions of pounds. The fact that these massive transactions take place in mere seconds may make many of us blush, but these trades take place every day between hundreds of privately owned banks all over the world.
Every trade between banks is made on a specific date and at a specific rate, and it is these agreed-upon rates that are reflected in the larger forex market. Rates adjust based on supply and demand and are "floating," which means there is no fixed location, such as the NYSE.