YES, it is legal and you should have had a receipt that you could print off too.
I have done this every year and it never a problem because the fact that it is taxed shows up immediately on the ANPR thingy the bobby's use and also on the national database.
Just go on as normal...... 
No, it is not legal. The offence is 'failure to display a tax disc'. The online exception being as specified earlier. I don't give a rat's arse what you heard down the pub from your mates mothers brothers dogs cousins owner.
Anyone trying to say otherwise is wrong, and irresponsibly opening up members to possible prosecution by trying to make out it is fact.
Of course, whether you would get caught is a different matter, and I suspect you'd be suffering from your own attitude issues should the police take it further. But the law is quite clear on this. You must display a valid tax disc at all times the car is on the road, except in the very specific instance of ordering by phone/internet before your previous one ran out, and this exemption is only from 1st to 5th of the month. It matters not if you have bought one, or lost it, or had your homework chewed by the dog.
If you need a tax disc immediately, there are ways, such as local DVLA office.