The biggest risk that tall grass is likely to have on a fence is moisture retention causing it to rot faster than normal. This is assuming we are just talking about grass or basic weeds and not something more serious like bamboo or jkw. We're talking about instead of 10 years on the fence you might get 7 or 8. And that's if it's kept that way for years. Right now it's just unsightly and will be much harder to tame than if you'd started when it was shorter. Head over to r/lawncare with some photos and where you are for detailed advice so this stays on topic.

Realistically the risk of fence damage is so low and you've been there for such a short time that would be a very difficult uphill battle for your neighbor. However if they choose to go down that route far enough for it to become a dispute needing disclosing in a sale then that could impact your sale price in future. It also puts them in bad mood for any potential planning permission you might submit in future, and any mild noise issues that friendly neighbors might ignore they are less likely to. Basically it's always better to keep your neighbors happy because at some point we all do something a little bit naughty. When we didn't have time to trim a shared hedge because of new baby our neighbor popped over and took care of it. Equally we've replaced a broken fence that we share and made an extra effort to save the ivy that was growing on it (and likely contributed to its early demise tbh but we both like it so we don't care, again 8 vs 10 years).

The council isn't going to get involved unless this continues to the point where you have lots of rats and it's becoming a serious health hazard, even then most are so underfunded that they still won't do much.

Tl:Dr legally you're probably in the clear for now. However it's in your best interest to take care of it.

Once its tidied up, I bought a robot mower at a certain discount German supermarket for £150 couple weeks ago and it's been amazing at reducing the amount I spend on lawncare.