I think most of these replies are going off the thread title and initial few lines and are missing the question the OP is actually asking. Lots of posters are answering telling him to not buy the unfinished house that he's already not buying???
He's already indicated in the OP that he's found a different house he likes (which isn't available yet) and he is asking about the mortgage.
I.e. Does he break the chain and stay in his current house for a bit longer or does he move into rented accommodation (which may mean he loses his current mortgage deal).
@Transform_IT
The negatives:
It's not looking too promising that you'd be able to keep your existing mortgage deal if the other house you're interested in isn't available till July.
Also short-term rental is likely to be more expensive than just staying put in your own house (unless you're perhaps in a large house, sticking stuff in storage and renting a much cheaper place for a bit.)
The positives:
You'll have sold your current place, less faff trying to find a new buyer (how difficult or easy was it first time round?)
Maybe a marginal benefit in that you'll not be part of a chain so would be a desirable buyer for the house, maybe moot if it's another new build though.
I guess you get to not let down the rest of the chain but really, this wasn't your fault, these things happen and obvs you shouldn't need go out of your way to the point of losing thousands yourself. Is the mortgage a particularly good deal say a 5 year+ fix etc.. how much would short-term rentals cost in that area vs staying put given you could be in one for 6 months? Extra faff to find a new buyer but also extra faff to move, not fuily settle in/unpack and then move again 6 months later (then again stuff in boxes already so...)
edit:
Obvs lastly, it's not guaranteed that the chain would break, 6-month delay might still be workable even if they're miffed about it, in which case I'd try and get an offer accepted for the new house asap (moot again if it's another new build).
In fact, if it's another new build and you can almost deffo buy it this summer then maybe just push back on your buyers "sorry guys but delayed for 6 months" and see if they're still happy to go ahead... they may want you to go into rental accommodation but that's also an option they can take too!