My guess is that her bank got suspicious and tipped off HMRC, she told me she had almost finished paying off her mortgage with the supplementary money she earned escorting. Big red flag as to where the money is coming from.
That does sound a likely scenario. Someone who starts paying in significant sums of money, on top of their regular PAYE income, is going to raise a flag. So HMRC will be wondering where this money has been coming from, especially if she has not registered for self assessment. The bank transfers are far easier to investigate than anonymous cash deposits.
As others have noted, the current tax year has not yet ended. However, anyone on self assessment is required to pay tax in advance, part by end of July and part by end of January (effectively pay as you go during the tax year, rather than the taxman having to wait a year or more for back payment). So, if she was earning extra income during the previous 2022-23 tax year, and failed to declare it, she will almost certainly also have failed to declare her projected earnings for this tax year, and failed to make the advance payments. Which may be why they are already looking at this year's unexpected income. If she is receiving income that she could reasonably have been able to predict when she made her previous tax declaration, then she will already be owing money that is racking up a hefty interest rate. And of course if she has failed to register for self assessment, that will also incur penalties.
HMRC are not interested in the OP, just interested in why he made the payment to the person they are investigating. But as others have said, it would be advisable not to behave in a way which could cause them to become suspicious of him. If someone is non cooperative, the investigator will likely start to wonder why. Even if someone has done nothing wrong, just having to complete several year's worth of historical income tax declarations is a lot of hassle.
Some years ago, I started earning some extra non taxed income. I dutifully reported it to HMRC, but despite several reminders, I got no tax demand. I finally realised, just in time, that they were waiting for me to miss the deadline for registering for self assessment. After which no doubt they would have stung me with the penalty and back interest. Of course, it is your responsibility to check if you are required to register, HMRC will not prompt you to do so.