One does not need to be FCA authorized to charge interest on an occasional loan to a friend if you are not in the business of making consumer loans.
This turns out to be a less straight forwards question than it would seem to be. This used to be regulated primarily by the Consumer Credit Act (1974) (discussed here), but now, the scope of that regulatory regime (and other financial services industry regulatory regimes) is governed by the Financial Services and Markets Act (2000) (Regulated Activities) Order (2001), as amended.
Offering credit to consumers is defined a lending money to an individual, but the licensing requirements that used to be imposed by the Consumer Credit Act (1974) only apply to activities within the scope of the Regulated Activities Order.
If you aren't within the scope of the Regulated Activities Order, you are subject to most of the substantive rules of the Consumer Credit Act (1974) (which is a comprehensive statute similar to scope to the Uniform Commercial Code in the U.S., rather than a narrow consumer protection statute of the kind found in most parallel legislation in the U.S.), but don't need a license and can lend to a friend at a non-usurious rate, on terms permitted by the 1974 Act.
This is codified in Section 19 of the Financial Services and Markets Act (2000) which requires that transactions which are "regulated activities" be engaged in by an "authorized person" or an "exempt person".
A regulated activity is defined in Section 22 of the Financial Services and Markets Act (2000) as follows:
(1)An activity is a regulated activity for the purposes of this Act if
it is an activity of a specified kind which is carried on by way of
(a)relates to an investment of a specified kind; or
(b)in the case of an activity of a kind which is also specified for
the purposes of this paragraph, is carried on in relation to property
of any kind.
Therefore, lending to individuals is ordinarily "consumer lending" which is a regulated activity, but only if it is "carried on by way of a business".
Also, a relevant provision of the Regulated Activities Order appears to be Section 17, which provides that merely lending money in and of itself is not always a regulated activity.
So, while the law could be more straight forward about it, it appears that the licensing requirements that would prohibit you from making consumer loans without a license apply only if you carry on an actual lending business, rather than merely making an occasional personal loan, in the same way as the now defunct licensing requirements of the Consumer Credit Act of 1974 were restricted to "Consumer Credit Businesses".
Therefore, you can loan money to a friend and earn interest on it in the U.K. even if you are not licensed.