My husband is Italian and I'm an African living in Italy with permanent stay. Can I travel to UK without visa?

A couple of people have deleted their answers about article 10 residence cards because it is not clear whether you have an article 10 card. But we can answer the question conditionally: You can enter the UK without a visa if you have an article 10 card and you are either traveling with your husband to the UK or joining him there.

Your card is an article 10 card if it says carta di soggiorno di familiare di un cittadino dell'unione, which means "residence card of a family member of a union citizen."

The conditions for traveling to the UK with an article 10 card in lieu of a visa are given on the UK government site at Entering the UK as the holder of an Article 10 residence card.

It is unusual for EU countries to issue article 10 cards to the family members of their own citizens, but it does happen. Some countries have decided to extend to the family members of their own citizens the same rights that they must grant to family members of other EU citizens, and Italy is such a country, so it is in fact likely in your case that the card is an article 10 card.

If, however, you established your residence in Italy before you met your husband, or independently of your relationship with him, then it is rather more likely that you card is not an article 10 card. In that case, you will need a visa. You can apply for an EEA family permit, which is free of charge and (supposed to be) issued under a simplified procedure.

As has been noted in the comments, the requirements for you to enter and remain in the UK will end at some point after the UK leaves the EU, so if you plan to travel after January 31, you should pay close attention. Alternatively, if you do not want to be bothered with paying attention, you can apply for whatever visa is appropriate to the purpose of your trip (which you will also need to do if you will be traveling to the UK without your husband).

If your travel is after the Brexit date, there might be problems.

We do not know when Brexit will be, it might be this Thursday, and we do not know which, if any, transition rules apply. While it is probable that there will be an orderly transition period and that EU citizens and their dependents won't be turned away at the border, anything is possible.

Whether or not you need a visa to travel to the U.K. depends on which country's passport you hold and the purpose of your visit. This U.K. government website will help you determine the visa requirements: https://www.gov.uk/check-uk-visa