Posted: 06/03/2015 at 18:01
I agree with Verdun and Stevie that membrane would almost certainly not work in this instance & that cultivation & zapping are the only way to go.
Do you know how long the plants have been there Foxy? If they are still (relative) babies (say 1 - 3 yrs old) the root systems will be much less developed and much easier to dig out. If, however, they are established plants it will be harder to eradicate them.
I suggest you dig the 2 beds over systematically & thoroughly as soon as you can and try to remove every last bit of the root systems. Then go back and dig them again in 2 weeks time - you will almost certainly have missed some. Assuming the beds are relatively small I, personally, would repeat the process a couple more times at 2 - 3 week intervals - depends how keen you are. By then we will be into early summer so I would take Verdun's advice and perhaps put some annuals in for this year & apply weedkiller if any new anemone growth does pop up.
I suppose you could pack pots of lavender in the beds (if the pots would be hidden by the box hedging) and just lift them out every couple of weeks to check for new anemone growth - but I would probably be more inclined to go with the annuals
I would hope the programme of planned cultivation and systemic weedkiller could eradicate the problem in one season but, if it doesn't, I am afraid there is little point in planting the lavender until you are on top of the problem.