Great question @persephone and welcome to the forum.

Each manufacturer is responsible for the noise figures which they quote in their specifications. The better ones will be accompanied by small-print which describes how it was measured.

However, the actual noise emitted will depend on how it's been installed. Sound will be muffled by vegetation or reflected off flat surfaces.
It's the installer's responsibility to position the external ASHP unit such that the regulations are complied with.
The installer should be MCS accredited, and will refer to the regulation MCS-020.

I believe that the crucial measuring point is the nearest window of a neighbouring property. So if the heat-pump is positioned ten metres further down the garden, then the sound will be significantly less of course.

MCS are consulting on changes to that regulation, which can read about here on their website.

The Building Regulations also contain requirements regarding noise, and Building Regs Part-E covers sound insulation within a property.

What heat pump noise a neighbour actually hears will be greater if their own house doesn't comply with Part-E.

We were discussing this just a fortnight ago in a topic about rule changes for heat pumps, which I suggest you look at.
That would be a good place to expand on the question you've just asked here.

Then just last week, @editor announced that he's compiling a video on ASHP noise.

@transparent

Why doesn't the government just issue everyone with earplugs? Simples. 😋

@derek-m They wouldn’t hear of it!

@transparent Many thanks! This was really helpful. My question is actually about the heat pumps that do not fall under permitted developments and are not compliant with MCS Planning Standards. My local council states that it is not necessary for heat pumps to comply with MCS, despite the fact that my neighbour (the owner of the heat pump) claims that the installer is MCS certified. My neighbour has provided my local council with a noise assessment that proves compliance with 42dBA at source. I do not understand what the 42dBA is. Isn't it the permitted development criterion? If it is, can it be used for an installation that is non-compliant with MCS? I am really confused.

Let me try to unpick that question, @persephone.

Your local council appears to be giving the correct advice, but it hasn't quite enabled you to appreciate what they're telling you!

a: You do not have to employ an MCS-accredited company (or individual) in order to install a heat-pump.
Indeed, you are at liberty to buy a heat-pump off-the-shelf and install it yourself.
That costs a great deal less, although you cannot take advantage of any Government grant of course.

You can buy a recognised brand, such as Mitsubishi, from a reputable UK-based wholesaler like Midsummer.

or you can buy direct from a Chinese manufacturer using the Alibaba payment system and reduce the cost significantly.

b: Any heat pump installation must comply with Building Regulations and Planning Rules.

For these, you can apply to your Local Council in the same way that you do for an extension/conservatory.

You will need to read the relevant Approved Documents for Building Regs, but they're available for download free of charge.
Here's Part-L which covers Conservation of Fuel and Energy, for example.
You will need to employ a qualified electrician to connect the mains power, for which you will be given a Part-P (electrical safety) certificate.

And you can also download a Dept of Energy Report/Advice on Heat Pumps and Planning Rules which they published in Nov'23.

c: Lots of other websites specifically address the rules concerning the 42bBA sound pressure level.
Those regulations must be adhered to, whether or not a MCS-accredited installer has undertaken the work.

d: MCS-accredited installers have the advantage that they are allowed to install heat-pumps without first applying for Planning Permission.
Their work is deemed to fall within Permitted Development Rights.

@persephone, this might of interest to you: https://renewableheatinghub.co.uk/forums/government-schemes/a-call-for-fair-and-legal-heat-pump-installations-in-the-uk