"Reminds me of the tax-deadline when online filing came in. Everyone tried to do it on the last day. Don't. Do it before that. Your teacher wouldn't have accepted the excuse back in school."
Or when the same happened with VAT - with the last date for submitting returns being 7 days after the old end of month deadline.
Back near the start, I tried to submit a return for a client the day before the new deadline, and the server wasn't coping with the load - so I printed the error pages. Being kicked out when the office closed, I decided to take the figures home and submit from there - but my internet connection was down, and service wasn't restored until it was too late.
Unsurprisingly, teacher - in this case HMRC - didn't accept the excuse, and hit the company with a charge.
The subsequent tribunal, on the other hand, took an entirely different view, and described the situation as ludicrous - IIRC, the wording went something along the lines of "It's ludicrous that they are unable to predict and cope with the demand, and then fine the registrant for being unable to submit returns as a result."
The bottom line is that it doesn't matter one jot if you can apply (or, in the case of tax/VAT returns, submit) one day, one week, two weeks, four weeks, whatever period before the deadline. The deadline is the deadline, and you are perfectly at liberty to leave it until then - and if their service can't cope, it's their fault, not yours.
Although, as you say,
teacher UKGov won't accept that as an excuse - possibly unless, as in my example, they are legally challenged. At which point, if it's a big enough cock up, they'll just legislate in their favour.