"What we want to do is to get rid of the backstop and that is the most important thing. We will also want changes to the political declaration which sets out the future shape of the relationship between the UK and the EU," Boris Johnson said during broadcast interviews on Tuesday.
The spark for the protests was planned legislation, now withdrawn, that would have allowed people to be sent to mainland China for trial, despite Hong Kong having its own much-respected independent judiciary.
Britain occupies a pivotal place in a bloc of European states that have tried to broker some resolution to a broader conflict between Tehran and Washington over the fate of a 2015 deal with the world powers designed to prevent Iran from obtaining a nuclear weapon.
Britain has denounced Iran's seizure of the oil tanker in the Gulf on Friday as a "hostile act", rejecting Tehran's explanation that it had seized the vessel because it had been involved in an accident.
The European Union said on Tuesday that Britain could be heading for a potentially disorderly exit in just 10 days time as Prime Minister Theresa May met with ministers to thrash out ways to break the Brexit deadlock.