Twist does indeed mean Damascus. For those unfamiliar with the term, the barrel was made before deep hole drilling was feasible by wrapping iron or steel strips around an iron rod (mandrel) and welding them together by heating and pounding with a hammer. As you might surmise the strength of such arrangements varied; at best they were moderately strong, at worst they were an accident looking for a place to happen, and many have blown up with modern shells taking the shooter's fingers along for the ride.
It is a good bet that the gun is Belgian. As Jim says, it was common for makers of cheap guns (some sold for as little as $2) to put on a fake name that resembled that of a quality maker; deception was intended and often succeeded.
Another good bet is that any gun barrel marked "fine London twist" is not fine, and never was anywhere near London.