Back to update - visited over the weekend and as expected, we loved it.
Funnily enough, we preferred Amersham-on-the-Hill to Old Amersham, which we didn't expect. Old Amersham is undeniably beautiful but we would prefer to visit for the shops and restaurants and be in New Amersham for the station. We also loved the New Town town centre. In any event, we can't afford Old Amersham.
We drove past a few of the houses shared on this thread and around different areas. We didn't like the Mortens Wood/Sheepfold Lane area, it felt very cramped and just not nice at all. However, we did notice that the area around there (First Avenue etc) can change quite quickly as you drive around. Some parts are really nice and then others are like Mortens Wood/Sheepfold Lane. That was similar around the New Road area. Completely understand @Ponyclubgirl 's point about that area. The good thing about it though is that it is in the Chestnut Lane/Elangeni catchment.
We drove and walked past the Station Road house a few times. The house itself looks good but DH is massively put off by the main road. However, with our budget we are likely to have to make a big compromise just to get into Amersham. We can then make improvements and hopefully sell for more down the line so we can move to a property we would be more happy with.
We preferred the Stanley Hill house (also went to see), as it is more set back and the road is wider, as @TizerorFizz pointed out. However, the no central heating issue is the big problem. Even if we decided to instal central heating, the cost is likely to spiral from whatever quote we get once the work starts as you cannot know what will be uncovered. We are also concerned as to why they haven't installed central heating after all this time. It indicates to us that there's some sort of issue.
All in all, a very helpful visit and we plan to continue visiting to help us to learn more and clarify what we want/what we are willing to compromise on.
We are also going to book a hotel and stay for a few days so I can do the commute into London as DH is concerned it may be too long and we will have moved for not much better if a commute!
Didn't mean for this post to be so long!