Rustle - I was intrigued by your first post and only changed my reply because it got me thinking. A quick check of Irv's helpful questions and answers revealed
"On a simple PPL, the Air Navigation Order stops you flying IFR in classes "A through E" controlled airspace, leaving "F" and "G" ('the Open FIR' to use an old term). "
Now what seems to follow from that is that in the UK you cannot file IFR in class D without an instrument rating (IMC or IR), and to avoid any confusion I mean in VMC conditions because what you file (IFR or VFR) has nothing to do in itself with the metrological conditions. I do not see, simulated or otherwise, how you can fly a procedural approach (in VMC and with a safety pilot) without being IFR because even if your entry to the procedure was VFR surely by definition you must become IFR once the approach starts. Presumably that means in the UK without an instrument rating there are no circumstances in which you can fly a procedural approach in class D except with an instrument rated pilot who is acting in his P1 capacity or under training with a QFI. Of course there are some approaches in the UK not in class A or D so for those all would be well - EGKA for example.
Now how does that change in Europe. Well the IMC is not longer valid as an instrument rating so your priviliges are no different that a non instrument rated pilot. L2K is in class D (I think) so presumably you have no business to be there IFR and strictly you cannot fly the approach without being IFR even in VMC.
Presumably in Europe, much as in the UK, what you can do is file IFR so long as you remain outside controlled air space and of course reamin within your metrological entitlement.