I did online renewal for my daughter on Thursday 14th April & sent docs signed for. They were scanned on 19th. Passport application approved 22nd, printed & delivered by 28th April.
It was soo much quicker than I expected. Bootle is where her old passport had to go!
Fingers crossed for you.
Having spoken to a few friends who are still waiting but applied before me it seems to be a hugeee deliver on first time passports!