Was just wanting to make sure that they accept a screenshot of my credit card limit as proof of funds
To be safe, I would probably take your actual statement with the £700 bill on it as well, just in case they don't think the screenshot is good enough evidence.
Since you have an £8,000 limit, a £700 bill won't be an issue, because the remaining £7,300 is more than enough to cover a 10-day trip anyway. And if you have the screenshot which shows it's already been paid, all the better.
Chances are you won't be asked to show any of it anyway, but it's best to be prepared
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One other option: do you have much money in your current account? If you have some money in there too, you could also take a bank statements as well, to show how much is actually available in your bank account (rather than being available as credit).