European prohibitions on bullbars on public roads

The answer to your question does not depend on what the laws of the UK, other countries or even the EU say about bull bars. The reason is simple: All of those countries signed the Geneva Convention on Road Traffic. According to Wikipedia, by signing the Convention, those countries agreed to respect each others technical requirements. As a result, any car registered in the US that meets US technical requirements can be legally driven on the roads of any country that signed the Convention. Thus, those countries are required by the Convention to allow you to drive with bull bars on their roads.

The power of the Convention was illustrated a few years ago when Florida passed a law requiring all foreign drivers to have an International Driving Permit. Since the Convention requires signatory countries to respect the licenses of other countries, Florida had to back down from enforcing its law.

The restriction pertains to their sale in the EU. The rule in art. 4 is basically

In accordance with Article 10, manufacturers shall ensure that frontal protection systems either fitted as original equipment to vehicles placed on the market or supplied as separate technical units comply with the requirements of Sections 5 and 6 of Annex I.

Possession and use are not prohibited.