When digging them out, go down as far as you can. Then go a bit further. Then a bit more. Loosen the soil even further. Then take a firm hold of the crown and pull slowly, wiggling it gently to loosen it. Sometimes you get the whole lot! And sometimes you don't.
It is possible to beat it, but you have to be thorough and vigilant, and if you're not going to be there to spot and remove regrowth then it's not going to happen.
'If you have a garden and a library, you have everything you need.'
I agree with others that the piles of stones, it ain't a rockery, need to be removed and the area levelled and turfed. Tenants are unlikely to be interested in keeping somebody else's garden up for them. Mowing the lawn is likely to be the limit.
Yup, I’d offload the stones on Gumtree or Freecycle as well. I’d put down a clearly defined edging to the lawn, put gravel around the raised beds, make a big bank of foxgloves in front of where the dog is standing and smother the rest of the soil (bottom left of photo to the bank of foxgloves) with some geranium Rozanne. Underplant the geranium with daffodils.
I would remove the stones, dig the area over, removing the weeds, make the soil level with the lawn and sow grass seed to extend the lawn. Tenants rarely care for a garden adequately.
I've gone back up the thread and had another look. I am not sure you have a 'rockery', so much as a 'place where someone has dumped a dug-up concrete foundation in lumps and not disposed of them'.
IMHO, it may be a lost cause for now trying to get rid of the alkanet, as it will certainly come back under tenants. But I wonder if it would work to remove the lumps, as previously mentioned, then rather than trying to turn it into a bed to plant up, put in some shrubs? These will be easier to care for and while the tenants are in they will simply develop, as long as you pick varieties that are right for your conditions (sun/shade, moisture, soil type and pH) and that won't outgrow their welcome. Also they will be able to compete with the alkanet.
The best way to control a thug like alkanet 'in absentia' is to arrange for it to be mowed regularly. That will at least limit its ambition. In a shrub border, it will probably thrive and that won't necessarily trouble the shrubs, if you pick the right ones but it won't be controlled and it will try to take over. If you were going to stay there, I'd go with the shrubs - much nicer. As you're not, I think a tenant will manage a nice easy lawn more effectively and/or it'll be easier for you to pay someone to cut the grass once a fortnight to manage it for them
Gardening on the edge of Exmoor, in Devon
“It's still magic even if you know how it's done.”
When I was doing my HND at Pershore, we had to do work experience over the summer. While some of my classmates worked at Dixter, Lambrook Manor etc, I worked in a private house in Darley Dale where I literally spent the entire time digging up alkanet! Despite that, I still think it's quite pretty for a weed.
"What is hateful to you, do not do to your neighbour".
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It is possible to beat it, but you have to be thorough and vigilant, and if you're not going to be there to spot and remove regrowth then it's not going to happen.
IMHO, it may be a lost cause for now trying to get rid of the alkanet, as it will certainly come back under tenants. But I wonder if it would work to remove the lumps, as previously mentioned, then rather than trying to turn it into a bed to plant up, put in some shrubs? These will be easier to care for and while the tenants are in they will simply develop, as long as you pick varieties that are right for your conditions (sun/shade, moisture, soil type and pH) and that won't outgrow their welcome. Also they will be able to compete with the alkanet.
“It's still magic even if you know how it's done.”