We just had the same thing happen except ours is a more palatable 1.6k which we can pay out of his salary from April. I think PP is right, this arrangement via self assesment has to be done online before 31st Dec, and I think the max amount is quite low, 5k sounds right. So my OH said two things:
At the start of the year the tax office never know what bonus you are going to get. Because of the various personal limits and tapering they have to do, they do this by adjusting your tax code throughout the year. He has had a couple, and a couple of times they started taking extra money. But then it got to the tax return which he is obliged to do (just over 100k) and they now know he had the bonus but I guess they didn't know quickly enough to get all the tax back before April. Basically, they are rubbish at tapering personal allowances.
The second thing is that it turns out the £50 a month on his pay slip for a mobile phone isn't actually taxed by his employer, so they are taking tax for that too. Deeply unclear on his pay slip.
We have had tax changes three times this year:
His employer forgot to include a voucher bonus on payslips, HMRC then took £34 a month for several months.
Then we had to pay tax for health and dental they had thus far failed to tax, the amount was about £178 but for some utterly bizarre reason, they are taking £66 a month for 8 months. I can't even...
Then, finally, the December 'you owe us 1.6k' at the end of the year, which they will take from April at £134 a month.
The OH tells me that he won't have to submit a self assessment next year because that is changing (under 150k) but we should expect these frequent pay amount changes to continue, because that system is not going to change.
I suggest you prepare yourself for this to happen in future years if you are likely to continue to get bonuses.
I hate their systems. They don't even tell you what you haven't been taxed on. We have spent six hours this year trying to figure it out for ourselves, because when he tries to call them, he is on hold for an hour then gets cut off.