Without any advanced notification, you can transfer £10,000 per day via bank transfer, £10,000 a day via card payment and £10,000 per day to a Monzo contact. So if HMRC can take card payment and banks with Monzo (!), you could theoretically pay £30K per day = 10 days of payments, without any other card/bank/Monzo being paid during.
Best to tap on ‘Request a limit increase’ at the bottom of the Manage Account screen and set up a one-off payment of £300K with Monzo prior to it needing to happen: (Example screenshot from my Monzo Personal Max account → ‘Manage account’ → ‘Limits and allowances’, values may differ between accounts)
Top limit for Faster Payments with most banks is £1m per transaction so I’d hope that Monzo would be able to cope with a single payment without resorting to CHAPS if you get your allowance raised in advance.
For that amount though I’d be setting up the payee, sending a tenner, amd checking it arrived with HMRC before sending the rest, even with Confirmation of Payee.