Ah! I answered the later question first.
I would first try to work this out with your neighbor, but if that didn't work out, check with your local council rules and regulations. Sadly, having to take legal action can result in a long term feud with your neighbor, in which you will have to act with absolute rectitude.

Ah, you didn't say that. That's ridiculous and the tree definitely will cause problems, lack of light being a lesser one.
Thinning it out won't prevent damage to foundations and drains. Ten feet is a mere nothing for a willow - does your neighbour appreciate how large its going to get?

Agree with Tug, try negotiation first and if that fails get some official help from Citizens Advice or your local council.

If you own your property rather than renting, presumably you have building insurance - if that's the case, take a photograph of the tree for ID of precisely what variety of willow it is so its possible to estimate height, spread and, more importantly, root spread, and showing its proximity to your property, then write or phone your insurance company about it. If you know where the sewer run for the houses is, and the willow is pretty close to that, that's a good reason for its removal - willow roots seek out wet areas, and will penetrate pipework over time. Your insurance company probably won't want to do anything to prevent damage, though will certainly get involved if damage occurs, but talking to them is useful from the point of view of then talking to your neighbour - if they own their house too, they should take it seriously.

It's much harder to argue over 'right to light' than it is to use the 'damage to foundations/property' argument.

I've had a similar problem with an ash tree next door only a foot from the fence as others on this site might remember. It's been cut down but not killed off so in another couple of years......

I've also noticed what appears to be a seedling from the large cherry only a few feet away from the ash tree site. I aim to chop as much as that off as I can once it gets level with the fence. They just aren't interested in the 'garden' next door and are clearly not bothered by tree roots in drains and foundations.