In the UK use of the Aerodrome Traffic Monitor (tower radar display) does not depend on the airspace classification. Many airfields in class G airspace (e.g. Prestwick, Staverton) use them.
Use of the ATM (in any UK airspace) is limited to:
1. Determining landing order, spacing and distance from touchdown of arriving aircraft
2. Assist in applying longitudinal separation for departing aircraft
3. Making sure that departures are complying with their clearance
4. Passing traffic information for circuit a/c
Airfields can apply to the CAA for exemptions to use the ATM for mode-C validation and various other tasks.
There is no requirement to provide an approach radar service in class D in the UK, although most places do. Many smaller airfields provide a procedural service at night; but this is becoming less and less common.
Hope that's of some help.