None. Fire safety of furniture imported to the UK is governed by the Furniture and Furnishings (Fire) (Safety) Regulations 1988. These Regulations are enforced by Trading Standards. HM Revenue and Customs liaises with Trading Standards on furniture imports as appropriate.
The European Commission's policy on standards is reflected in the General Product Safety Directive 2001/95/EC, where European standards are recognised as a means by which products can be shown to meet the general safety requirement. However, the directive also acknowledges that the requirements of national legislation (including mandatory compliance with national standards) take precedence in the absence of product-specific Europe legislation.