I agree, Woofgang, but there is no specific law that actually states that parking across a dropped kerb is illegal. Any prosecution would have to be brought under the legislation that prohibits 'causing an obstruction' and that would be very unlikely to happen unless a complaint was made where the dropped kerb exists solely to provide access to a private driveway (rather than, for example, to assist wheelchair users getting onto a public footpath).
The police know that many people will park across their own driveways when another household member's vehicle is already on the drive (or permit a visitor to block their own vehicle in by parking across the driveway). It would be crazy for them to bring a prosecution for 'causing an obstruction' under such circumstances. Similarly, in the questioner's circumstances, they would probably assume that there was no objection to a vehicle being parked across the driveway unless they actually received a complaint.