Can an employer prevent employees from displaying support for a particular political party at work, for example by wearing a badge or t-shirt?
Generally, an employer can enforce standards of dress that it considers appropriate in the workplace, which could include prohibiting items displaying support for a political party. Guidelines on this could be set out in a dress code policy, or a policy on political activities in the workplace. In particular, employers may want to enforce a policy that prohibits such items for public-facing staff to avoid creating an impression that the employer's organisation endorses a particular party or political view.
It is unlikely that an employee could claim that being prevented from displaying support for a particular party is discrimination because of their religion or belief. Support for a particular political party is unlikely to be a "belief" protected under the Equality Act 2010, but a belief based on a political philosophy could potentially be covered (Grainger plc v Nicholson  IRLR 4 EAT). Even if an employee's political belief is found to be covered by the legislation, a claim for discrimination is likely to fail if the employer can show that the prohibition of displays of support for a political party applies to all employees regardless of their political views, and that the reason is to avoid disruption to the workplace, or to prevent the intimidation or harassment of employees or customers.