This is an invasive process, and its use to deceive others arguably constitutes a "search" under the Bill of Rights Act (the Law Commission certainly thought so in its Review of the Search and Surveillance Act 2012). So you'd expect the police to have some idea of how often they do it, right? Wrong. According to an OIA response,
Police do not hold statistics as to the use of this form and as such your request is refused pursuant to section 18(f) of the OIA as the information requested cannot be made available without substantial collation and researchThere's also no approval process, and no formal guidance on when police can seek to assume an online identity. Its just completely unregulated, left to individual officers running investigations, with no oversight or monitoring whatsoever. Effectively, random plods are making up the law as they go along. Which does not seem like a good way to manage an invasive search power.
If we took steps to ban or regulate this practice, the police would no doubt claim it is a valuable investigative tool which should be left alone. But without even basic statistics on how often it is used, they simply have no empirical basis to make that claim. Without guidelines, they have no basis to claim that it is used only in circumstances where it is lawful and proportionate, and without an approvals process, they have no basis to claim that it is used only in those circumstances. In the absence of such things, given their past track record on such issues, we're entitled to deep, deep suspicion.