Might fall foul of your 'not too heavy' politics requirement but I love my Private Eye subscription.

Options:

• New Scientist - I used to read it religiously and you get the right balance of detail and digestibility, at least for me. Others could find it to be a bit too much.
• BBC Science Focus - not read it much but it's a lighter read than New Scientist without dumbing it down.
• Fortran Times - covers science and archaeology developments as well as odd news and out-there weirdness often with tongue firmly in cheek.
• History Today - one of the leading history magazines
• BBC History - another accessible history mag from the Beeb. They produce a few others that could be of interest: Countryfile, Sky St Night, Wildlife and Music.
• Prospect magazine - not read it but it's a popular general-interest magazine that doesn't dumb things down.
• The Idler - it may be of interest but it's come and gone a few times since I last read it.

Best bet might be sampling a few and see what tickles your fancy.

Does your local library membership include electronic magazines via an app like PressReader? Mine does and there are a ton of free magazines of all genres. In general they have the last three months worth of issues and it might help you find one you like before you buy a paper copy (if indeed that's your style). Subscriptions are nearly always massively cheaper than buying in the shops.

I particularly enjoy Uncut, as being the best of all the music magazines IMHO. One of the only ones I read cover to cover is Linux Format. And I have a subscription to Retrogamer, but to be honest that's not very good anymore and I won't be renewing it.

This is likely to be an unpopular suggestion because of who it is and it being a paid service, but Apple News+ has actually got me back into reading magazines for the first time in at least a decade.

I’m already locked in to Apple because of all the family’s devices, so I pay for Apple One which covers all the family’s music and storage subscriptions etc, but one of the elements I get more use of than I ever expected are the magazines available as part of News+.

There’s a ton of them available such as National Geographic, Time, Empire, New Scientist etc, which I regularly read. Probably better experienced on an iPad rather than a phone due to the format, but it’s been great to have access to all of them without having to buy a physical magazine, although that may actually be what you’re after.

There’s a list of the publications here, some of which are crap, but a lot of which are things I would read if they were to hand on a coffee table.

Apple News Publications

Anyway, the reason for the recommendation is, there’s a lot of choice, and since it’s essentially a paid subscription to all of them, you can easily sample some and see which publications appeal.

The Guardian does a weekly magazine of their long form articles. I’ve impulse bought it a few times when going on long journeys and it’s very good.

I’ve considered subscribing but it’s £18 per month (discounted from £27 for the 1st year) and that’s a lot for me.

If you're into music production, I find Computer Music & Future Music both to be interesting enough to keep me looking at them

Others people have already mentioned in Private Eye & New Scientist

suggestions because i think they're well written, no political inclination intended - always read a broad range of opinions

• The Economist (I find the whole thing a bit too much, too niche, but for core articles it's very well written and sourced)

• Readers Digest - fantastic variety of short human-based stories

• National Geographic - same

• Spectator - for a certain point of view

• Guardian Weekly - for a certain point of view