You asked

At what point within a month is data on prices taken to calculate the inflation statistics relevant for that month?

For example, in April 2017, the CPI and other inflation statistics will be announced for March 2017. At what point during March are price data taken to represent the state of play for that month?

We said

Thank you for your request for information about the timing of our price data collection. The figures for CPI, CPIH and RPI are intended to reflect prices on one particular Tuesday of the month (either the second or third Tuesday). The majority of prices are collected on this day. We are unable to give out this information in advance of publication, because of the hypothetical risk that service providers or retailers may change their prices to influence inflation.

We publish the exact date alongside the latest figures under 'publication policy' in the background notes of the consumer price inflation statistical bulletin:

https://www.ons.gov.uk/economy/inflationandpriceindices/bulletins/consumerpriceinflation/jan2017