Is it normal to leave the old external render on and just plasterboard over?

In many extensions this is usually the case. As long as the render was sound you will never have any problems. But it should be included in your quote if they were to remove it. Yes it is a money and time saver for both you and your builder. As they won't have to spend hours removing the render. Clearing it up.Then getting rid of it. Just to gain an inch or two which will hardly be noticed.

If there is no need for it to come off then there’s really no point in taking it off , if space really is that tight then ask the builder to remove it but be in agreement with them as to wether it was in the price or it is going to be a extra charge to remove

Remove it! Csn cause damp and can't bond to it qe went to a job and happened to gain alot of mold! Many thanks lkp

Yes that is normal happen and no need to remove the existing rendering . Because the render will be a good grip to hold the plasterboard .