I have often seen furniture marketed as ‘in the style of’ for example, Charles Eames. Is this permissible under UK Design Law?

Purely under a UK design law basis, the issue would concern the appearance of such furniture rather than its branding, therefore marketing such furniture in that manner would not offend against any design law.

However, any potential issues that may arise could be in respect of trade mark laws or passing off. If, for example, a famous name was registered in respect of furniture, then it would essentially depend in what manner you were using that name, i.e. you may not be using it in a trade mark sense (i.e. to distinguish your goods from a competitor), but purely to denote a characteristic of your goods, as in the example above, and hence not offend against the registration. However, each case will depend on its own facts, and whether for example that use is honest.

Furthermore, if the trade mark was a really well known mark, then it could be said you were taking unfair advantage of that mark even if you are using it to denote a characteristic.

If you are in any doubt about what is permissible, seeking legal advice is recommended.