1. No amount of insulation will stop pipes from freezing eventually if the temperature surrounding the pipes is at or below zero. All the insulation does is enable the water in the pipes to retain any heat it has for a longer time.
2. If you are worried about internal pipes, insulate with the usual foam. Up to a point, the greater the wall thickness of the insulation, the longer it will keep the water from freezing. The very cheap lengths you can get in "sheds" is too thin, go for 19 - 20 mm wall thickness.
3. In lofts, try and keep the pipes below any loft insulation, to the point of building a (hardboard?) tunnel over the pipes and relaying loft insulation over the tunnel. Make sure there is no loft insulation underneath any tanks, so that they receive some heat from the building. Insulate the tops and sides of the tanks.
4. Externally, well insulated pipes touching the walls of the property may survive overnight if well insulated. However, the only way of stopping pipes from freezing is to bury them at least 600 mm underground.
5. If none of the above is any good to you, look at trace heating.
