What is Member doing in the UPDATE clause??   I assume that you meant
to say Accounts as a table name; the singular names are used for
scalars, so member must be a column name.

UPDATE Accounts
SET  activated = 1
WHERE EXISTS
(SELECT *
FROM Members AS M
WHERE  Accounts.account_id = M.account_id)
AND  SHA1(Accounts.account_id + Accounts.email_address)  =
Accounts.p_uid
AND Accounts.activated = 0;

I tried to fix the mulltiple names for the same data element.  There is
no magical, universal "id" in  a valid data model; **what** does it
identify?  Read any basic data modeling book.

I had to guess at the tables from which the columns were taken.

You do not explain what SHA1 is  - UDF?

You seem to be writing SQL with bit flags.  SQL programmers do not use
low level. asembly language constructs.  That went out with file
systems about 1970.
You might want to Google the syntax for an update statement.

Are we supposed to guess as to the product and version?

I guess Mauve. Version 1.3.

BTW: In any anguage ... this contains no looping structure.