if you put a thick enough layer on of bark then it should be ok. but if it is a very windy site or you have a cat that might dig it then go for slate.

Don't waste money on those membranes. They don't work. Weeds grow up through them and on top of them and they are a hassle to deal with. A couple inches of pea gravel or slate chips might work - and they won't break down. You can also use planters with pelargoniums or some nice annuals - campanula?

Thanks both! Another dilemma then! several cats around and the weeds might grow through the membrane anyway! Maybe just an extra thick layer of slate then?

You won't get weed growth through the membrane - there aren't any pernicious weeds in that area, I assume. Its only things like bamboo, japanese knotweed, docks and the like that punch through a membrane. However, it is possible you will get weed growth on top, once an organic mulch (like bark chips) starts to break down and weed seeds blow in.

You can use slate, with or without a membrane, but it does nothing for the soil. You will also, eventually, get weed seeds germinating in that, because soil will blow into the slate over time. You could use organic mulch straight onto the bare soil and just top it up as it degrades - at least it will be improving soil conditions around the tree and indirectly providing nutrients for it.

Also bear in mind yours is a deciduous tree - collecting soggy leaves off a pile of slate chippings is no easy task... there's no perfect solution I'm afraid!

I've tried using the membrane and it has zero affect on weeds. The weeds will grow through the membrane, causing unsightly rips & tears as you try to pull them up as will a garden hoe or straight rake as you try to clean up debris. This is not 'hypothetical assumption' but actual experience. Trying to remove or replace the membrane afterwards is a bloody nightmare. I only suggested pea gravel or slate as an alternative, but there are many other options. A simple garden rake or leaf blower will take care of fallen leaves - again I speak from experience.

Weeds will eventually grow on top of any suppressant. Dust and dirt will blow around and settle amongst the gravel, slate or bark and the weed seeds follow pretty quickly.

I'm glad I didn't rush out to buy membrane! Sounds as if organic mulch and a hoe will be the best bet after all! No short cuts! Hadn't thought about the leaf problem either, or weeds coming up through membrane or setting in the slate! Thank you all very much. Back to basics and regular hoeing!

Containers with shade tolerant planting might be attractive on parts of your mulch if it looks a bit bare and could be removed when you need to move the leaves in autumn. It would also cut down the area weeds can seed into.
I wouldn't touch membrane with a barge pole.