You can be laid off for 4 weeks with the RP9 form, then have to return it to the employer stating you wish to claim redundancy and they have a week to get back to you accepting redundancy or offering you a minimum of 13 weeks work within 4 weeks of that date. So technically you could be laid off for up to 9 weeks as long as the company can offer you 13 weeks unbroken work.
It seems though that they are only offering 12 weeks part time though, which to me looks like you would be eligible for redundancy if that's what you wanted. Not sure on the details of the 4 week redundancy package though.