Did you get the EICR in the end? If so, what did it say for the type of supply? (TN-C-S, TN-S or TT)?
If they were purpose built flats then a suitable earth should have been provided (and it's possible there is foundation earthing or similar in place). Do you know when they were built?
The main issue of concern with your reading would be to ensure that it is a suitable earth rod or equivalent and not provided via copper water piping or similar. That should have been checked at the time of an EICR, though it can be difficult if there is common piping.
Even if the DNO couldn't provide a PME supply at the time, they may be able to now - though it can get complicated with flats as sometimes the building management has responsibility for internal stuff and not the DNO.
If you don't already, you will want to be checking your RCDs work by pressing the test button very 6 months to ensure they are still in working order.
If you can provide a picture of your consumer unit and your main fuse head/meter, it may be clearer, depending on how things are wired....