The choice of avoiding fancy lifting or blended body or leading edge extensions designs is also a clear design choice: "SKYLON differs from other spaceplane configurations in several key respects. Apart from the unique propulsion system, the main difference is an aerodynamic configuration that comprises a definite wing plus body. This was selected because it proved to be more optimum in terms of weight, lift and volume than the more fashionable blended bodies frequently portrayed for spaceplanes."
So it seems implied that the choice of wing design has been done intentionally and with deliberation. From the drawings, though, I guesstimate the wing area of the main wings to be around 150 meters square, though I suppose some design changes may possibly occur later.