Thanks for the responses! 
A couple of women I spoke to today, said they would not tell him, because he would want to spend it. And even though they're quite comfortable at the moment, they would go downhill fast (financially) if they lost a wage. So they'd like to keep most of it for a safety net. They'd pay debts if they had them, but if not, just keep it for emergencies.
My cousin's DH has been pining for a motorbike for a year or so, and they really can't afford it, and would struggle with the upkeep (maintenance/fuel/tax/MOT etc,) on top of their car, and she said if HE got wind of an extra £10K or so, the first thing he would do is buy a motorbike. And then some golf clubs and a subscription to the local golf club for 3 years! He wouldn't think 'hey that money could be a financial buffer if we get into trouble.'
I don't think it necessarily shows a problem in your relationship if you kept it from him. Everyone keeps SOME kind of secret from their partner.. Also, it seems that the women more likely to keep quiet about it (from women I have spoken to,) are the ones who are not well off financially, and they are cautious about it being spent on unnecessary things... and they'd rather save it for emergencies. If people are quite wealthy (£100K income+ per year between them,) then £7,000 to £12,000 is a drop in the ocean.
Not sure what I would do. I feel like I would say I had won something, but if it was £12,000, say it was £5000. Then have some fun and treats with the £5000 whilst keeping the £7000. Not for me, but for a time when we really really need it.
Like with many men I know, DH would probably squander it, and put it towards a new car that we DON'T need. Or book a £4,000 cruise! I am more frugal and grounded and would keep it for emergencies. Around half of it anyway!
I am not sure about the 'splitting it' idea that as been mentioned. What if you won £12,000 and split it 50/50, (and had £6,000 each,) and he just squandered his £6,000 on fluff and crap, and you had YOUR £6,000 still intact? Would you share your £6,000 with him if he had spent HIS £6000,and he suddenly needed money for something? I mean REALLY??? No matter how much you love him/care about him. Would you share yours if he spent his half?
Be interesting to know how many really would share their own £6,000 in real life. (Once their partner squandered his.) And even if they did, if they would be deeply resentful.