Labour stats are published monthly. Immigration stats are quarterly. Neither appears to be missing. I’ve seen allegations like that floating around social media but they don’t seem to hold up to scrutiny.
The Labour Force Survey releases are here, most recently published on Friday:
Release schedule – Major economic releases
The immigration data seems to have a number of different products, but the quarterly estimate of non-tangent resident was last published in June:
Estimates of the number of non-permanent residents by type, quarterly