I live in the UK and often hear that a lot of places are "no-drone zones" meaning flying a drone there could get you a penalty.
Is there any database for these zones as often signage isn't clear?
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There are two considerations on whether you can fly somewhere - airspace restrictions and land restrictions.
Details on the airspace can be acquired from a number of common sources - the CAA has a page with lots of in-depth information here1, but there are a lot of third-party websites and applications which present information in a more accessible format (for example, I personally use Drone Safety Map and the NATS Drone Assist app.) Remember to check for NOTAMS, although many websites and apps provide this functionality too.
Land restrictions are not so neatly centralised, so you will need to manually investigate whether your local authority or playing field owners have any restrictions for flying drones from their land. As drone use has increased in recent years, larger numbers of public spaces are making this information available on websites or signs but in many cases, you will need to find out who is the owner and contact them directly for permission.
Whilst, not an official source, this website: https://www.noflydrones.co.uk/ (no affiliation) provides a community update list of restricted places but to be sure it is usually better to search for the specific place to see if you can fly there.
Another consideration is the open category your drone falls into. Either A1, A2, or A3.
Which category it is will be based on the weight, max speed, and who built the drone; and will determine how close you're allowed to fly to uninvolved people.
This potentially allows you to fly up to 5m from uninvolved people if you've got a speed limited drone but requires no uninvolved people at all in the flight area if you've built your own drone over 250g.
Page 4&5 of the CAP 1789 document has more detailed information on open category classification.