What is the best way to accept credit card payments over the phone and get the transactions into Quickbooks in the UK?

Online Banking does it for you, user51506. 

QuickBooks has the Online Banking feature that allows us to connect a bank or credit card account into QuickBooks. We'll have to do it on the computer or mobile web first, and once connected we automatically sync any information in your mobile app. 

I'll show you how to connect: 

1. Log in to qbo.intuit.com.
2. From the Banking menu, click Banking. 
3. If it's our first time to connect it, select Connect account. Click Add account if we already linked an account in QBO. 
4. Enter the bank's name or URL. 
5. Select Continue and enter you bank credentials. 
6. Click on the bank we want to connect and select the account type from the drop-down. You can click +Add new if it's not on the list. 
7. Follow the onscreen instructions to successfully connect the account. 

Downloaded transaction are from as far as 24 months. From there, we can assign, add, or match transansaction. If the credit card account is not on the list, we can manually upload then from a CSV file.

You can check out this article on how to record customer payments. 

Let me know if you need anything else. Thanks!