Bain of my life too Town.
Some information. Chrome plated or polished stainless warmers put out less heat than white. These are not designed to heat the space. They, unsurprisingly, are designed to warm towels.
Just look at the difference in design of a radiator and a warmer. The surface area of a radiator is what makes it an effective heat source and that's orders of magnitude more than a warmer.
If you have a cold bathroom you will need suplementary heating in the form of underfloor heating or a proper (separate) radiator.