If you have a mixer tap in the kitchen the casting may have perforated allowing mains water to feed into the hot water system OR the coil in your hot water cylinder has perforated. Turn off the mains water and see if the tank still overflows, if yes its most likely to be the cylinder.
When you say the small water tank in the loft, do you mean the smaller of two cold water tanks with ball valves? If so, another possible cause might be "overpumping" from your central heating system If your pump has variable speeds, try turning it down.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!