If the provider was unable to provide primary cover would they have to discontinue any service?
Not necessarily. MATS Part 1 says...
1.6 Limiting a Service
1.6.1 Outside controlled airspace in circumstances where controllers cannot continue to provide the following primary requirements:
a) traffic information and traffic avoidance in respect of all conflicting unknown aircraft for a radar advisory service; and
b) traffic information in respect of all conflicting unknown aircraft for a radar information service, controllers may elect to continue to give the service by limiting the extent to which it is provided.
1.6.2 Controllers must inform pilots when they limit the service and ensure that pilots are made fully aware of the implications of any limitation.
1.6.3 In particular the service should be limited when:
a) the aircraft is operating within 10 miles of:
i) the edge of the radar display;
ii) weather clutter; or
iii) permanent echoes.
b) the aircraft is operating in an area of high traffic density;
c) the aircraft is operating near to the limits of solid radar cover; or
d) the service is being provided using secondary radar only.