Similar experience, but the Great Tit had been eyeing the nest box up first. However, after the Blue Tits had already claimed it, there was an incident recently where I heard an almighty argument between the Great Tit and Blue Tit that was already successfully nesting there. !!
I thought it was a Crow making all that noise, unbelievable! In the end the Blue Tits won though and have definitely produced Eggs, They are hatched now as parents are relentlessly flying in and out all day, and I've witnessed one of them flying out with a faecal dropping obviously from one of the chicks.
Delightful to watch, I'm addicted and obsessed with them. I'm purchasing a Sonic Cat Repellent device tmrw as I've a nuisance Cat that I need to deter in view of the potential fledglings really soon.