In a legal sense, not having a known-ice aircraft is going to impose far more restrictions on flight planning than not having a full IR.
In a plane not certified for known ice: if one is willing to risk climbing through freezing layers (which is generally fair enough if it is stratiform, one has a deiced prop, and the layer is evidently 1000-3000ft thick) then a full IR would help to get on top in much of UK's airspace.
Personally I find that I cancel flights if the 0C level is below the MSA, and flying a non-deiced plane in those conditions is something I wouldn't do. A full IR would still cause me to cancel.
I absolutely do not accept sweeping statements like "if you are going to plan to fly in IMC in the UK, you need a full IR". Trained to the privileges, and equally current, there isn't going to be much difference. Most noncommercial IRs you bump into are long lapsed, and you can be sure their currency went a long time before that
And what plane is the man with the gold-plated ATPL going to fly in IMC? Let's say it's a rented wreckage of a C172 with knackered avionics and no autopilot. That why sweeping statements are misleading.