I've just spent ages searching ebuild for one of the couple of threads where this was discussed but I can't seem to find them.
Short version: we first introduced ourselves to all our neighbours when we moved in. Had them around en masse for Christmas drinks etc (I should add: this wasn't just a ploy to help us getting planning permission - we'd have done this anyway).
Over time, we introduced the idea of extending, then significantly extending. We then moved on to the general idea of replacement in view of the costs of such a large extension. By the time we actually went for planning, everyone in the immediate vicinity expected us to be replacing the bungalow with a new house, so that wasn't a surprise (avoiding surprises is, in my opinion, the biggest key to reducing the chance of objections).
It's a common mistake at this point to be open with your neighbours about your plans, and to invite their feedback. This would have been my approach had I not been counselled strongly against it by our local architect. He pointed out that once you ask for feedback, you plant in people's mind an expectation that you'll take their feedback into account, not matter how unreasonable it is or how much extra it will cost you. Most people will want you to make your plans smaller and more conservative, if they agree to them at all. Then when you say you can't or won't, they become emotional and object. Worse, you might have different people asking for different incompatible changes, in which case you're bound to disappoint someone even if you're willing to compromise.
In the end, we told people we'd show them what we were building before we submitted the planning application, "so you know what we're doing". A couple of days before submitting the planning application, we provided them with an impression of the roadside view from Sketchup (the house is set back quite a long way and partially concealed by a tree, so this showed the house looking very small in the street scene), along with a letter setting out what we were trying to achieve. We talked about improving the street scene (the bungalow was pretty ugly, and we'd intentionally allowed the front garden to deteriorate!) and reducing energy consumption, but half of the letter was about the build itself. We explained how we were using a factory-built timber frame so it would go up quickly and with minimal impact on the neighbours. We explained that we would be onsite every day and welcomed any feedback about reducing the impact of the build on the neighbours.
In the end, we had no neighbour objections, and a couple of letters of support. The town council objected, but they always do when anything that doesn't look like it was built in the 1930s is proposed.
I have no evidence to support my opinion, but I believe that presenting the proposal as a fait accompli reduced the chances of objection, because people were less thinking about the planning application and more thinking about the (inevitable!) build.
We may also have been lucky with "objection fatigue". Two other nearby properties (including our immediate neighbour) did very similar things to what we were planning, and both faced significant local objections. I do wonder whether the fact that both of those ended up getting through left people a bit tired of objecting and losing. But I also think that how you present your intentions will nearly always help your cause.