The key question is whether the free piano is capable of being tuned. Can you enquire of the people you're getting it from - even if they then have to relay the enquiry to the owners - what its recent history is? If it was in regular happy use with stable tuning in the not too distant past, then the likelihood is it can be returned that way. If OTOH noone knows of anyone having playing it since grandma's grandma, it might be a dud.
I'm suspicious of the report that it's a quarter-tone flat but "in tune with itself". A quarter-tone is quite a lot, and pianos don't go that flat while managing to do so with complete consistency across the range staying in tune with themselves! One part of that claim must be bogus.
Ordinarily one would accept a freebie and see, but the problem with a piano is not so much the tuning fee, as the hundred or two you'll probably have to spend to get it moved.
In fact I might even suggest doing things back-to-front as an insurance policy: Ask the owners if you can get a tuner to come and tune it where it currently is, THEN, if all is well, have it delivered. The tuning will cost you fifty quid or so, but if it proves untunable then you will have saved the delivery fee, which will be a lot more. If it's not too far away, you might even then be able to get it delivered without needing to be tuned again.
The problem with leaving it and seeking to buy a second hand one is you'll likely have the same problem anyway. Cheap second hand pianos are often way out of tune, and then you're still left making a judgment call about whether they're tunable. Or you buy one ready-tuned probably from a dealer, but it will cost more.