In the UK you can recover only your economic loss, which is less than most people think and, for a private person, can be very low indeed.
Against that you have a duty to mitigate your losses so e.g. if a plane is grounded through illegal/unsafe maintenance, and the engine goes rusty inside as a result, you (probably) can't claim for the engine because you had a duty to protect the thing during the AOG time...
As a general comment, maintenance is a tricky area and while I don't support this for a moment, I can see the CAA's passive stance. Most of the UK flight training industry, and many private owners, operate old wreckage, which is simply uneconomical to maintain to "paperwork perfection". And the capital to replace it with newer stuff is not available.
So a lot of maintenance is done "on the nod". You can do it overtly, with INOP stickers on avionics, Or you can do it illegally, usually with the owner's consent/direction, by ticking boxes and not doing the work; this is widespread but not usually unsafe since most maintenance requirements do not directly (on a fixed wing) impact safety.
A lot of CAA/EASA maintenance requirements are simply stupid e.g. if I was on a G-reg I would need the o-ring seals in the emergency gear release valve changed every 2 years; these have a life of 20-30 years and no plausible means of preventing the valve's success in dumping the system pressure and lowering the gear even if they are leaking. This is an all-day job which costs about £1000 and most people cannot do it correctly because it is fiddly, and eventually the threads on the hydraulic fittings get stripped and then you have a ~£5000 bill...
Not doing ADs is illegal and stupid, but even then there are things which are pointless safety-wise e.g. seat belt life limit ADs when the seat belts are in a perfect condition.
And much depends on the owner's attitude to resale value. With many planes this is so low that trashing the resale value by not doing ADs is not a huge issue. It just hits the next owner...
If the CAA got totally pro-active on this they would shut down GA as we know it. The issue is not shutting down the cowboys; it is the owners who in most cases ask for this level of maintenance. Most MOs are quite capable of returning the plane from the Annual with a gold plated elevator - if you ask them to do it.
Then there are the crooks who are told to do XYZ and who do only X and charge you for XYZ, but they would probably claim that they were acting on verbal instructions, and billing for labour is very hard to pin down.
Maintenance is a tricky area. GA planes are not BMWs which you can drop into a BMW dealer and expect a reasonable job done. There are good firms and bad firms, but all owners need to understand what needs to be done and work with the MO to agree a schedule. It is simply not possible to leave the plane parked outside and collect it a few days/weeks later. Not unless you are very lucky.