Even Heathrow is in Class D airspace.
In the UK, it just means that with an IR(r) you cannot enter airways.
Why is bit beyond me, because self navigating in class G airspace is in my opinion much harder than flying under IFR in airways. You have to plan your route very thoroughly, can't always get on top, have to watch airways base altitudes, minimum safety altitudes, skirt around zones you are unlikely to be granted an IFR transit at particular altitudes (due to airways above), keep changing LARS frequency and kindly ask for a service from each one on your route, giving your details several times on route etc... It really is quite hard when you are in solid IMC.
Whilst flying IFR in airways, life is much easier, you get handed over between controllers, given GPS / VOR waypoints and altitudes to follow, get a guarantee of a service being provided, and although you should always verify clearances, you are unlikely to need to manage MSA or routings.
Anyway - CB means "Competency Based". CB-IR is the name of the COURSE and not the RATING. The rating is the IR(A) which is the same if you sit your IR(A) course, or if you sit your CB-IR course.
If you sit the CBIR written exams rather than the ATPL exams, your licence will be annotated with CBIR, stating that you are restricted to non HPA (high performance aircraft) due to the lack of exams. Otherwise you will be issued with an identical IR(A) with no annotations.
I hope this helps.