The authority to issue penalty notices has been around since 2004 and is in the Education Act.
The relevant Statutory Instrument
https://www.legislation.gov.uk/uksi/2024/210/made
(3) Where no penalty notice has been issued to the parent under section 444A(1) of the 1996 Act in respect of the same child in the preceding three-year period, the amount of the penalty is—
(a)£80, where the amount is paid within the period of 21 days beginning with the date on which the notice is received;
(b)£160, where sub-paragraph (a) does not apply.
(4) Where a penalty notice has been issued to the parent under section 444A(1) of the 1996 Act in respect of the same child in the preceding three-year period, the amount of the penalty is £160. (5) “Preceding three-year period” means the period of three years ending with the date on which the penalty notice is issued.
So if you've already been fined once in the last three years, it's doubled. And
An authorised staff member who becomes aware that a relevant entry of absence has been recorded in a school’s attendance register in respect of 10 sessions in any given period of 10 consecutive school weeks in respect of a child
So it doesn't have to be all in one go - or even one term.