Joanne, although well intentioned, is, I think, wrong, the actual volume of noise legally doesn't matter. If you look at the guidance on this site you'll see that it is defined as noise which is causing a nuisance. I'd argue that a noise which is preventing you from sleeping could quite reasonably be defined as a nuisance, despite it's low volume.

My advice is, if you have the courage, approach your neighbour, try and avoid being too accusatory and just express the discomfort at being kept up to 5am. If you can't approach them, consider writing them a letter. Keep a log of dates/times and if all else fails phone your council - they're legally obliged to help you out.

We had noise problems with our neighbours, they didn't respond to our verbal and written requests for peace so we phoned the council who wrote them a letter which cited specific dates and times (we'd kept a record of). Although this hasn't been 100% successful (they were noisy again last night) they have definitely reduced the frequency of their noise and seem to turn the volume down a lot earlier than previously.

There is hope so have courage.

Peace.

sounds like there boiler. I have the same issue

maybe its cannabis factory and its the lights and fans you hear. you never know! have they got kids?
i thought my neihgbours were using a drill verey night it turned out to be a very loud and old hoover

Honestly, there's nothing you can do. It's not "high level" enough to seriously bother the police and if they do come, they'll just brush it off. It's not loud enough for the authorities to care. While it may be annoying, there's pretty much nothing you can do. You can try snooping around but if they catch you, compliment them or something so they won't get irritated and keep the thing on forever. This is from my experience though and I sincerely do hope they stop whatever it is they're doing.