The answer is yes, you can import products with a logo on but it is not quite as simple as that. We all see Logos every day, but importing products marked with them is complex topic.
First and foremost it depends on the logo. If the logo is your own Intellectual Property (IP) such as your company logo, you must ensure you have documents proving you have the right to use it. The reason for this is that often, unknown logos can be mistaken for a counterfeit version of another brands. If you do not have documented proof showing this, the goods may be seized and destroyed by customs, and the importer may be prosecuted. If you have proof that you have the right to use the logo, then importing goods with it on should be absolutely fine.
On the other hand, importing goods with famous logos on can be more challenging. Let’s say, for example, you decide to import mugs printed with a Manchester United logo. Firstly, if you have not bought directly from the owner of the IP, in this case Manchester Utd FC, you must obtain permission to have the logo printed onto your mugs. If you fail to do this, you can be sued by the football club, who own the logo.
The second, and more complex step would be to assess the value that the logo adds to the mug. If importing plain white mugs, they may be valued at £1.50 each… whereas importing Man Utd branded mugs they may be worth £2.50 each. This is due to the licences and the royalty that would have to be paid on the sale of the goods which increases their value. This means you may be required to pay more duty and VAT on the product when cleared through UK Customs. This is something you must enquire about before importing the goods as if you fail to declare the goods properly you may end up with customs issues. Customs may seize and/or destroy the goods, or you may just end up paying more than you had originally bargained for.
With copyright of IP there are some grey areas. The copyright for your IP is only valid in the country they are registered. This would mean if a logo is copyrighted or patented in the UK, others may have the right to use it abroad without breaking any laws.
If in doubt, Check out this booklet produced by HMRC on IP rights or ask UK Customs and they can give you a definitive answer.