The Daily Telegraph and the Daily Mail complete the top three, with 307,690 and 237,381 tweets per week respectively.
"It's important to us to see our journalism reaching new audiences and finding people where they are, so it's encouraging to see the results of this study," Laura Oliver, UK social and communities editor for the Guardian, told journalism.co.uk over email.
"We use a mixture of automation, which we are always tweaking the recipe for, and hands-on editors looking after what we share via these accounts.
"Some of our fastest growing accounts are those that have more hands-on editing, but it's about finding a balance and our team of editors keep an eye on what goes out automatically."
Oliver said automation is a way for the Guardian to stay on top of the numerous stories it publishes, while at the same time allowing the team to explore different sharing options and presenting stories in different ways.
"Importantly, we're always looking at the reception of what we do using in-house analytics and Twitter's own insights," she added.
The Guardian is using an analytics platform called Ophan, which looks at social traffic, referrals, and attention time among other metrics.
It is designed to give journalists the information they need about their stories at a glance, informing editorial decisions.
Oliver said that aside from looking at the Guardian's own Twitter accounts, sharing stories should also be made appealing for the audience as well.
"It's important for us to understand what type of stories and issues repeatedly perform well when we share them on Twitter or when they are picked up and posted by readers.
"This might help us make decisions about when we tweet something, relevant hashtags or keywords or existing communities on Twitter that we should be working with.
"We shouldn't overlook the fact that we also want to write good digital headlines for our stories, this benefits search and social."
The study by Searchmetrics looked at data relating to 11 UK newspaper websites, counting the average number of tweets their stories generated each week.
Here are the results:
1. The Guardian, 392,358 tweets per week
2. The Daily Telegraph, 307,690 tweets per week
3. Daily Mail, 237,381 tweets per week
4. Independent, 214,868 tweets per week
5. The Mirror, 113,194 tweets per week
6. Financial Times, 61,065 tweets per week
7. Daily Express, 24,165 tweets per week
8. Daily Record, 11,107 tweets per week
9. The Times, 8,772 tweets per week
10. Daily Star, 6,556 tweets per week
11. The Sun, 3,531 tweets per week
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