The people at Twitter have simply had enough of the Britain First account that was on their website. They believe that the account is in violation of their terms and conditions, and they have taken steps to suspend the account.
Twitter has not publicly shared why they have suspended the account, but they generally do not do things like this unless they have reason to believe that the account is in violation of their policies. Some of those policies include the exclusion of material that is pornographic in nature or material that is considered hate speech or bullying. Any of those activities could land you on the banned or suspended list on Twitter.
It is also against the rules to be an account that is associated or affiliated with a group that promotes hate or violence says CNN. Therefore, this may have been the marker against which the account was suspended.
Britain First is a political organization in the UK that is considered far Right wing and has some views that most decent people find disturbing and repulsive. They believe that Jewish people are the cause of a lot of the social problems in the world, and they have very anti-immigrant views.
The anti-immigrant views that they hold have been what has been attractive to Donald Trump and some of his supporters. The belief for them is that Britain First is just telling it like it is when no one else will do so. They look to this political party as something that should perhaps be emulated by leaders in our own country.
The group is so far from the mainstream in Britain that they rarely get more than a few dozen people to their rallies and protests. They also have been deregistered as a political party in the country. They have no elected officials at any level of government either. Therefore, the organization is largely irrelevant in the United Kingdom. However, they regained a little bit of attention when the President did retweet some false or misleading videos that the group put out on its own Twitter account. After that happened, the group thanked the President for what he had done, and the White House had to backtrack a bit on what had happened.
Now that Twitter has taken the action to suspend the account, you might imagine that there will probably be some kind of anger from the group as they use Twitter as a primary means of getting their message out there.