You can accept payment via credit card only if you are a merchant with an agreement to a merchant acquirer.
However, if this is for a personal transaction, can't the payer simply transfer the money from their credit card to your bank account using its sort code and account number?
If you're an online merchant, you don't need a terminal. You can just process payments through your website.
You'll still need a "Payment Services Provider", which can be a bank, such as Natwest Streamline or Barclays Merchant Services, or an intermediary such as Worldpay or Paypal.
Our business has a Paypal account and we can transfer money to the bank very quickly, as that URL states. However, setting up that bank transfer process was a bit of a pain. It was some time ago, however, so now it may be far easier ...