It is a criminal offence ( in the U.K.) to drive a car without third party insurance cover.
What’s the law regarding flying?
Same thing applies for flying in Sweden at least.
EU law:
Insurance in respect of liability for third parties
For liability in respect of third parties, the minimum insurance cover per accident and per aircraft depends on the maximum take-off weight (MTOM) of the aircraft. This takes into account that the potential damage on the ground increases with the weight of the aircraft. For aircraft with less than 500 kg MTOM, the minimum insurance cover is 750,000 SDR. For aircraft with 12-25 tons MTOM (e.g. regional jets), the minimum insurance cover is 80 million SDR. For aircraft with 200-500 tons MTOM (e.g. long-haul jets), the minimum insurance cover is 500 million SDR.
Legislation
Communication from the Commission to the European Parliament and the Council: Insurance requirements for Aircraft Operators in the EU – A Report on the Operation of Regulation 785/2004 [COM(2008)216]
Regulation (EC) No 785/2004 of the European Parliament and of the Council of 21 April 2004 on insurance requirements for air carriers and aircraft operators
Commission Regulation (EU) 285/2010 of 6 April 2010 amending Regulation (EC) No 785/2004 of the European Parliament and of the Council on insurance requirements for air carriers and aircraft operators
What are SDR if I may ask?
Medewok, special drawing rights.
I assume one SDR is roughly equivalent to a USD?
The indemnity insurance we were all required to have in CZ before we could fly solo or rent someones plane, only covered us to 200 000 Kc (which is less than $10K), and it was worldwide cover.
1 XDR = 1,22€
The SDR stays more stable than individual currencies. IF the £ drops badly IF Brexit occurs, our insurance, in £, might become inadequate. (IF we were still in EASA.) 
Isn’t the required insurance cover itself insured, for the duration of the policy for which you pay in advance?
Is the reinsurance in £ or SDR? Or € or US $? I haven’t a clue.
