A 20-knot battleship was possible but demanding in 1882

Could Britain have built a 20-knot pre-dreadnought battleship in 1882?

Yes in principle, but it would need a much larger power plant, perhaps twelve boilers and three shafts, with major penalties in weight, space, fuel, and cost.

Contemporary battleships generally achieved about seventeen knots, so twenty knots was beyond normal practice rather than beyond engineering possibility. The design might need twelve boilers instead of eight and perhaps three shafts with triple-expansion machinery. The extra plant would consume displacement, crew, fuel, and protected internal space. Later ships approaching nineteen knots show the path was credible, but an 1882 vessel would pay heavily in cost and arrangement for the final few knots.