Can our company try to save money by leaving the heating switched off later and later every year, and telling us to 'wrap-up'?

Low, uncomfortable temperatures mean poorer productivity and, depending how cold it is, leads to a lack of concentration. This can lead to accidents – bad for staff and for the company.

This is of course all secondary to the fact that there is a legal minimum temperature of 16°C (though we'd recommend 20°C for office work), below which your employer needs to take action, or let you go somewhere warmer. The HSE website has information on workplace temperature.