My feeling deep down is that they didn't do a proper job to be honest. I would never expect weeds to grow in the middle of the tarmac within 1 year, let alone a few months. I'm not entirely sure on the spec as I trusted them to do the job properly after seeing all their good reviews online.
I know the top layer of tarmac is about 4 inches deep, maybe a bit more. But I don't know the thickness of the rest.
As above, I'm not too sure about the thicknesses apart from the top layer.
I have already thought about digging down to one root to see how deep it goes but I'm hesitant because I thought it might completely damage the tarmac that I dig up...
I think I'm going to get them to de-weed again first and may go for option 2 if it doesn't fix the issue.
Using house insurance never crossed my mind but that's an interesting option. I may look into this dependant on what happens with the company over the next month or so.
I did start to weed-killer it myself when I saw the weeds but got fed up and called the company to come back around initially. That's how the ball got started about my options from them.
I'm tempted to get the whole drive re-done but worried that the same thing will happen again! The refund/weed killer myself is a very tempting option right now.
I'm actually tried the WD40 trick already but it didn't do much good. But that might be because I didn't weed killer the root, only the top of the holes where the weeds were showing.
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Thank you all for your replies, very helpful! Taking everything on board right now.
Bit of an update... The company have agreed to try option 1 for now and then we can discuss further options later on. They said they can't do it until we've got dry weather (understandable) and it's been raining non stop lately by me (bloody typical!!).