I think you could be screwed either way in the long run.
The rules on a 1 storey extension have been extended so you can build so far back without planning permission.
There are plans afoot to allow people to build upwards on existing properties without planning permission.
In effect this would mean that someone can build a large extention now and ensure they do foundations which are deep enough and strong enough, and build in two phases over a number of years to bypass planning permission altogether.
With this in mind, I think even a 1 storey extension which doesn't need planning permission, could affect the value of your property as these changes and possible future development will start to be factored in, in valuations.
The preposed changes to planning may yet fail to materialise but I think you have to consider this as a possibility whenever you buy any property. The potential for any future development around it is always there and you may have little say in it. Planning laws is something that is liable to change over the next few years because there are housing shortages.
You can object as it stands to a two storey extension. You are within your rights to do so. There are no guarantees over who will win the case though.
I think the thing is, whenever you buy any property you have to be mindful that things may change during the time you live in it.
Whether it be houses being built higher up, reducing surface water absorbance and increasing the chances of your house being flash flooded or whether it be a question of over development which blocks your light.
In this sense, I think your reaction is over the top but I don't think you are unreasonable to be unhappy and object either.