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Conservation areas are mainly about stopping demolition and ugly accretions on existing buildings. It often happens that quite modern buildings are built in them. The alternative would be pastiche, and that's not really the point of designating the conservation area in the first place, as pastiche can look worse than something that's clearly intended to be different. That said, I can't remember ever seeing such a modern addition to a c.a. that I liked, but that's just me.
As Tenderloin says, it's easy to find out. There are maps on every council's web-site that show you the designated area down to the exact house. It's an essential step that you need to do first.
Thanks for the info @Oliver Schick I will raise it with the architect and the surveyor.
Judging on what's going on round here at the moment, I would be surprised if we were in a conservation area. There's currently a block of flats being built on a tiny plot of land (an unused garden essentially) on the end of our victorian terrance. I have no idea how that got past LA planning.