The Restricted Instrument Rating, also known as an IR(r) or IMC rating, is a sub-ICAO rating only available in the UK. Some refer to it as a ‘get out of trouble’ rating, or ‘get you home’ rating, because of it’s inferior status compared to the full European IR, BIR, CB-IR or US FAA IR.
I don’t know the history of the rating, but I suspect it came about to help private pilots and instructors work with the UK’s climate, which is often worse that many other places in western Europe. We suffer far more low cloud, than Southern France, Spain or Portugal, and so complying with visual flight rules can sometimes be harder.
The IR(r) only requires you to have obtained 25 hours flying experience since you applied for your PPL, of which 10 hours must be as PIC, and 5 hours cross-country flight.
The training consists of 15 hours flying, of which 10 must be with sole reference to instruments. There’s a theoretical knowledge exam, and a flight skills test. The rating is valid for 25 months, and can be renewed by carrying out a skills test.
As you can see, in training temrs, it really is far inferior to a full IR but it is an extremely useful rating. You can fly IFR in the UK only, except in Class A airspace. You can shoot IFR approaches to the published minima. The minimum visibility allowed at your arrival and departure aerodrome is 1500 metres, and they recommend that you play it safe, by having a minima of no lower than 500ft agl for a precision approach, and 600ft for a non precision approach, especially if not in a good practise.
If you keep in good practise, there’s no reason why you couldn’t do a cross country in IMC, fully expecting to take off and land in cloud. If however you don’t practise the skill regularly, then it does really revert to just a ‘get out of trouble’ rating that it has become so famously known as.