Hi Annie,
There are three ways I know of to sort this:
1) Install a small electric "on-demand" water heater in the bathroom. This would sort out the basin at the far end of the house, but you'd still have to wait for the shower / bath.
2) Install a recirculation loop pump. Basically you'd install a return pipe from the far bathroom to the hot water tank, and a small pump. That would keep all of the pipework warm at all times (but make sure you insulate all the pipework also, for energy efficiency).
3) Put electric "trace heating" tape along the pipe, then insulate on top of this. This has just enough electrical power to keep the pipes warm, so avoids the initial slug of cold water from coming through.
You pays your money and you takes your choice, basically!
How accessible are the pipes themselves, throughout their length?