The recently created Centre, which has been backed by Gary Lineker, Rachel Riley and London mayor Sadiq Khan, met with Twitter representatives on Wednesday to discuss excluding "hate actors from public discourse".
Ms Riley, who has been the target of online abuse, accompanied CCDH chief executive to meet with Twitter.
The pair advocated for Twitter to work in cooperation with CCDH on a new initiative to make it easier for users to share blocklists and to reinstate the ability to import and export lists of blocked Twitter users.
They also called for a full review of the Twitter accounts belonging to both Katie Hopkins and George Galloway, arguing that the pair used Twitter to spread hate.
The controversial commentator's account still displays retweets from other accounts, and a small number of messages that "this tweet is unavailable". Usually, suspensions of Twitter accounts include complete removal, which is not what has happened here. It's unclear whether Hopkins removed the tweets herself or if Twitter took action following the meeting.
Twitter has been contacted for comment.
The CCDH said it hoped she would be removed from the site. Mr Ahmed said: "There is a long road ahead before social media is made safe for dialogue, information exchange and the formation and maintenance of relationships. The fact parents are so hesitant and fearful of allowing children onto social media platforms shows how toxic many of these environments have become."
Both Hopkins and Galloway have a long history of courting controversy on Twitter. Food writer Jack Monroe was awarded £24,000 in a libel action against Hopkins in 2017, following a row over tweets suggesting Monroe approved of defacing a war memorial during an anti-austerity demonstration.
The former Apprentice candidate applied for an insolvency agreement the following year to meet the £500,000 costs from the case, causing her to sell her £1m home in Exeter.
CCDH published a series of guidelines in October last year urging targets of online abuse to resist the urge to respond, block them immediately and to report any potentially criminal content to the police.
Thereport, co-authored by psychologist Dr Linda Papadopoulos and Imran Ahmed, CCDH chief executive officer, said engaging with trolls was less about winning an argument than the trolls leveraging an opportunity to spread their propaganda as widely as possible.
"When a troll targets you for abuse, block them immediately; this will ensure that they cannot tweet at you ever again, and removes mentions of them from your notifications," the report's guidelines advise.
"If you receive several tweets in a short period of time, temporarily switch off app notifications on your mobile devices; this will protect you from unplanned exposure to troll hate."