Important considerations are that firstly, a new-build is zero rated for VAT, whereas renovations are subject to 20% VAT.
Secondly, its a good idea to take an objective look at the house you have and think about what will be left of the original fabric if you decide to go down the renovation route. For example, if you have a poorly built bungalow and wish to put another storey on top, as well as replacing window and doors, and insulating the walls, you will only have the original block-work walls left of the original building. In this situation a re-build is by far the most sensible route.
Trying to make existing cold walls perform thermally is going to be very difficult too as the thermal-bridge to ground cannot be easily avoided.
If the home you are considering renovation work on has some architectural merit, and the renovation work is not so dramatic, then it may be better to retain the original structure and so avoid the material expenses of rebuilding.