I need a new EU Spouse Schengen Visa for my Chinese wife for a visit to Spain. As per previous instructions, I've booked the trip for 7 July 2016 but vfsglobal have informed they have no appointments available in Manchester (we are based in West Yorkshire). Is there any other way to obtain the Visa so we do not lose the holiday and payment?
No perfect solution but there are a few things you can do:
Bypass VFS, as the spouse of an EU citizen (because you wrote "EU spouse visa", I am assuming you're a British citizen and she would be travelling with you), your wife is covered by the EU freedom of movement. It means that she is entitled to get a visa under a simplified procedure, not the regular Schengen rules and the consulate should be more accommodating.
And, in principle, it should not take longer than 15 days to issue this visa. It's possible that VFS isn't aware of all this but the consulate is really at fault if they can't find a solution. Don't be obnoxious but do remind them of that if necessary.
Suggest applying to another consulate (see Can I get an appointment at a French consulate different than the one assigned to my state?) Applicants are not entitled to it but consulates can always allow that and, as an EU citizen, you are in a stronger position to ask for it.
While waiting on the consulate to react/trying to reach them, keep watching the schedule, some time slots might free themselves.