Hi @Jel1983 and welcome to GADC.
As you mentioned, when it comes to airspace restrictions, Class D is no longer relevant for flying drones under 20kg. Currently, the only main areas you need to be concerned about, in the main, are Flight Restriction Zones (FRZs) which only apply to airports / aerodromes. There are a few others specific areas but the best way to make sure is to down load the Drone Assist App from NATS which makes it really clear, showing any current restrictions in the area you want to fly.
Of course there are other restrictions, when landowners do not allow take off and landing, but that is a whole different ballgame and the source of many a discussion in threads at GADC!