I found a legal firm in the UK who gave me some legal advice. (Cole and Yousef of Rotherham)
It would seem that sending in a new Visa application, this time insisting that Worldbridge include ALL the supporting evidence instead of leaving out 2 thirds of it would usually be quicker and easier than going down the Appeal route.
However, new visa applications usually take 15 working days (so Worldbridge say!) so why did ours take 78 days?
Well at this point there was only 2 weeks left before our flights, so this was not an option for us.
The solicitor gave me some advice on how to get in touch with the UK Border Agency. He said that there is no point calling the premium rate number as this only gets you through to the Worldbridge Agency Call Centre, who cannot / do no / will not assist in any useful way. (Which unfortunately I had already found out, the expensive way, 40 Euros lighter in my pocket)
The only way you can try to contact them is by direct email (which I tried and the mail just bounces back as undeliverable) OR to try contacting them through the Home Office website. http://www.ukvisas.gov.uk/en/
On this page there is an enquiries button at the top which leads you to a web based form. I used that.
I also informed them that I had sought legal advice, and stressed the urgency seeing as the flights are booked for in less than 2 weeks time.