They start inspecting holes in mid february, and will start building in late March (depending on where you are and what the spring is like). Earlier in the south, later in the north. They time breeding to coincide with the emergence of moth caterpillars in May.
I ring blue tit broods at 11-15 days old, and last year the first brood was ringed on 20th May and the last on 6th June. The year before it was 21st May and 8th June. That would put first egg laying at around 2nd week of April for the first birds. Nest-building, in a nestbox, will start in earnest 1-2 weeks before that. So, that's about the end of March for the first birds in Cambs.