That's what the strimmers are for.
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Interesting point, because I gather from highways engineers that their vegetation spending is being cut back, if you'll pardon the wholly intentional pun.
There is also the point that trees take 30-40 years to get to full maturity. All those motorways built in the late 60s and 70s are now having tree problems that they didn't have. Requiring more action (and thus expenditure) that the Highways Agency doesn't have.
The answer, as said previously, is cut them down, then strim every year. It's what HS1 does, and it works.
Well if it works then you'd hope there wouldn't be a need for a leaf fall timetable in places but there is.
The Cobham line has one and outside of the leaf fall timetable a lot of children for one of the local schools usually get off the 8.02 arrival at Guildford from Portsmouth and join the 8.07 to Waterloo, alighting at London Road. It has a 5 minute connection time which makes it an official connection and actually doable as the 8.02 is usually on time.
When leaf fall timetable comes into being, the Waterloo service via Cobham is due to depart at 8.04. To avoid missing it, some of the children, once they cotton onto the fact it's leaving earlier, then run knowing they can probably just catch the train in 2 minutes. Some do catch it and some don't. Not a good promotion for not running at stations though.
Not sure why there isn't a problem with vegetation on the line via Woking to London. You'd the k that would gain just as many trees, especially Guildford to Woking section.