What's the law on building an extension that blocks a neighbours window?

It's not so much a matter of "law" but of Local Planning Policy and interpretation by the Planning Authority (usually your local Council).
Many local authorities publish Guidance on what's permissible; try googling "guidance on residential extensions" plus the name of your Council.

My own area's document (which I know as we were consulted as a Resident's Association when it was in draft form) is very clear on this -

"Windows should not overlook a habitable room or garden of a neighbouring property and as a general rule there should be no new windows in any side wall directly facing a neighbouring property other than windows serving bathrooms, WCs and landings..."

But the Planning Portal is less precriptive, and suggests you ask local Planners. It's not even certain that your neighbour needed nor applied for Planning permission; it might be that they were advised that this was "permitted Development", or that they just put it up without permission, as Councils are sometimes too busy to enforce, even if they notice it. (we only stopped a major unapproved and illegal neigbouring upwards extension at a prior address by putting extreme pressure on the Council, at both Planning Official and Elected Councillor level, to enforce).

Either way and as if you proceed, you will need to consult your neighbour, and maybe pay for a Party Wall Agreement (google it) you ought to

- do your research; on general Planning policy (as in posts above) and specifically whether their address shows when you do a search of past Planning Applications on your Council's Planning website

- have a quiet word with them; knock or drop them a note with a view to saying hello. You don't even have to be to precise about the detail of your possible intentions; maybe just ask if they did the extension themselves, and if so, what other neighbours and the Council's attitude was, or might be to any plans of your own.

Of course it might be that they don't know because they bought the house as is, or are tenants, or that they are the kind of people who, having annoyed their neighbours with the noise and trauma of their own building project, will object to everyone else's out of sheer bleddymindedness.

In which case, do you want them as neighbours!?

I think, due to what you want to do to this property, I'd be looking for other properties more amenable to my needs. It sounds like you would just be walking into hassle with this one. There has to be an alternative without these problems.