Told that my wife could not have flu jab as well, is this correct?

Hi @bigfella,
My understanding is that your are entitled to a free flu jab if you are in one of the specified groups - eg if you are pregnant; if you have certain medical conditions such as COPD; and if you are a carer.  If you take a look at the NHS England website here http://www.nhs.uk/conditions/vaccinations/pages/who-should-have-flu-vaccine.aspx it sets out a definition of what they consider a carer to be - the main carer of an individual with a disability or an elderly person.  Presumably you would meet the disabled or elderly person criteria, and as you've explained your welfare is at risk if she can't provide the care for you that she usually does, I can't see how she wouldn't meet the carer criteria.  Maybe instead of asking a GP your wife could make an enquiry at the doctors surgery reception, explaining that she is a carer and she'd like to make an appointment for her flu jab.  If they are unwilling to arrange the appointment, my advice would be to ask the reception staff to check the NHS england website, and if that doesn't work try carefully wording an enquiry along the lines of "The way I read the criteria, I'm certain that I/my wife do/does qualify for a free flu jab - do you think I could have a chat with the practice manager and maybe we can sort it out?  I'd hate to have to make a complaint..."
Definitely worth following up, @bigfella, after all, she does meet the NHS criteria, so she is entitled.
Hope that helps.
Lucas