Is it OK for me to raise the soil level without removing shrubs

I'd be worried too. I don't think they'd appreciate being 'buried'. Maybe you could put some divider boards in and raise the empty areas only, leaving the shrubs and their surroundings as they are? Lavender, rosemary etc. like being planted in raised mounds.

That sounds like a plan! I have got some log roll going spare and could use that. The rest of the bed I'm particularly worried about is perennials with clumps of Alium bulbs (the tiny ones that multiply like crazy!) I am confident that I can dig those up and replant them, maybe splitting some up in the process, but the large shrubs are another matter

Not worth putting your back out trying to lift established shrubs! You might consider gradually replacing them instead - cheaper than years of physiotherapy!

I've taken cuttings of hebe, mexican orange and viburnum dawn last year, rather than attempt to move them.

If they are well established I doubt they will mind the extra depth of soil. It will act as a top dressing and give them extra nutrients. All three of them are toughies.

@Hetty58 - I already have fused vertibra from a slipped disc 8 years ago! You're absolutely right - if I really had to dig them up I'd let poor old DH do the heavy work

@Hetty58: Sorry, I've not quite got the hang of all the controls on this forum yet!

merlotgran that was my original thought, but then I read an article which said that, when mulching, don't put the mulch too near the stems. Or were they just referring to the softer stems of perennials? Has anyone else just raised the soil level around woody shrubs and was it successful?

The article means don't pack mulch around stems, especially young plants. As yours are well established I would just leave an area of loose soil around the stems so their drainage is not compromised.

aeration and drainage I mean.

All should be fine, as they are well established. 6 inches is not a huge amount. You could make a little ditch around the main stem, but I think they’ll be fine and probably respond well to the added nutrition.

Raising or lowering of the soil level around tree may result in the eventual death of a tree.
I'm not sure about shrubs but I would think the same rule could apply.

I have mulched shrubs but the layer has been no more than a couple of inches and often to raise the level a bit where the soil had become compacted.