Its possible that there is an earth through an alternative path, I can't actually see any main bonding in your pic, and by the lack of that, I would also suggest that there would probably be no supplimentary bonding in the bathroom either.
So its probably likely that its through the control electrics of the boiler, or the immersion heater, both these appliances have an earth wire connected and are bolted to pipes which run probably run through the ground
The problems in a purely physical way of looking at it (forgetting regs, etc) are the impedance of it is likely to be pretty high, which means a fuse might not blow, and secondly its going to be thin, thats bad enough if the impedance is low and its all over in the drop of a hat, but with something that I suppose could be passing 20-30A indefinatly until someone notices it could easy set on fire (of course it could be much higher impedance than ~ 10 ohms, but we just don't know), and of course the path could disappear if plastic pipe is fitted at any time
So this is probably how your socket tester was fooled (They are easy to fool, in certain borrowed neutral situations for example you can have it telling you that you have live and earth reversed

)
As to changing the CU, well it depends on the electrician, no one will work on it and leave it with major defeats, like missing main earths and missing main bonding, etc, but less major defeats could just be recorded, changing a CU is working on every circuit, so he has got to test every modified circuit and check that it is basically safe, but there could be stuff slightly wrong with them thats not dangerous that he just notes it as fixing it would not be feasable (lighting circuit with cable with no earth in, supplying only double insulated fittings for example), or stuff that he misses (flying splice with choc block in floor void for example), he is signing for an alteration, so its not quite the same as signing to say he installed things, but he still has to fully test things, its all about striking the right balence, a new CU with RCD makes things safer, but the electrician at least has a duty of care to tell you about dodgy stuff, and if its too bad and you say no to extra stuff he'll want to avoid being the 'last man in'
Also a shiney new CU means the installation looks a lot better to the untrained eye, and can lead to future owners being deluded as to what its really like, etc (there probably is no better way of hiding a dodgy installation from prospective buyers

- not that I condone this, but I certainly know it happens from time to time, the stories crop up on forums like this when people find it in a family member's new house... )
Its less than clear cut, and I hope this has gone someway to explaining the jusgement process behind things, of course it varies between electricians, some don't do CU changes at all for example because they don't want to call it, etc