The relevant legislation here is the Financial Services and Markets Act 2000 together with subordinate legislation passed under that Act.
Financial Services and Markets Act 2000:
(1) No person may carry on a regulated activity in the United
Kingdom, or purport to do so, unless he is - (a) an authorised person;
or (b) an exempt person.
(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 business and - (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.
(5) “Specified” means specified in an order made by the Treasury.
Financial Services and Markets Act 2000 (Regulated Activities) Order 2001:
The following provisions of this Part specify kinds of activity for
the purposes of section 22(1) of the Act (and accordingly any activity
of one of those kinds, which is carried on by way of business, and
relates to an investment of a kind specified by any provision of Part
III and applicable to that activity, is a regulated activity for the
purposes of the Act.
(1) Entering into a regulated mortgage contract as lender is a
specified kind of activity.
(3) In this Chapter — (a) subject to paragraph (5), a contract is a
“regulated mortgage contract” if, at the time it is entered into, the
following conditions are met — (i) the contract is one under which a
person (“the lender”) provides credit to an individual or to trustees
(“the borrower”); (ii) the contract provides for the obligation of the
borrower to repay to be secured by a mortgage on land; (iii) at least
40% of that land is used, or is intended to be used — (aa) in the case
of credit provided to an individual, as or in connection with a
dwelling; or (bb) in the case of credit provided to a trustee which is
not an individual, as or in connection with a dwelling by an
individual who is a beneficiary of the trust, or by a related person;
but such a contract is not a regulated mortgage contract if it falls
within article 61A(1) or (2).
The following kinds of investment are specified for the purposes of
section 22 of the Act.
Rights under a regulated mortgage contract.
So, if you are providing the mortgage to someone who will live at the property and are doing so by way of business (likely unless this is an arrangement with a friend or relative) then you will need to be FCA authorised unless there is an applicable exemption. See Chapter XV of Part II of the Regulated Activities Order and Section 38 FSMA and the Financial Services and Markets Act 2000 (Exemption) Order 2001 for examples of exemptions.
A full analysis of financial services regulation would be too dense to fit into a Stack Exchange post and you should seek specialised legal advice before considering entering into any kind of mortgage as a lender.
"is it even possible to do this once without a company that does this as a general product?"
It doesn't matter whether you are a company or whether you do it once or regularly. However, due to the costs and practicalities of obtaining FCA authorisation (where applicable) and ensuring that contracts and land registry charges are correctly drawn up (given the high stakes), you are unlikely to see many one-off or "amateur" mortgages in the real world.