I'd be cautious about them changing their mind on the second one after sending the first. But also that isn't the case here and "they" are two different entities.
Ok, last few mins the out going gov send out 1k. 10mins later the incoming gov send out 1k. You receive 2 checks of 1k on the same day from hm gov. Have you been lied to?
So if they sent you 2 checks of £1000 would that be breaking their promise?