An update.
After talking to http://www.consumerdirect.gov.uk/ , they advised me to go back to the trader (Carphone Warehouse) and quote :
Sale of Goods Act 1979 "fit for purpose made known" and that I was miss sold the product because on the back of the box it says "it's perfect for surfing the internet downloading, emailing, whether you are at home or using your laptop out and about".
The other very clear point of law is "The trader must sort out your problem, not the manufacturer", so it's Carphone Warehouse's problem not 3's.
Well, I called my local brand Bromley and quoted this. They seemed to be obsessed with pointing out "3" have a 3 day cooling off period based on coverage around your postcode. I reverted back to the blurb on the 3 box which specifically says "or using your laptop out and about". I mentionned I already had very expensive BT broadband hub at home, so this was to use outside of the house. They seemed to totally dismiss this. I asked to talk to the manager, and what a surprise (as with the Hammersmith Carphone Warehouse) it was the manager's day off. I asked for the area Manager... he was on holiday !! However, after pushing the sales assistant, he put his teamleader on.
The teamleader was helpful with only one thing, he told me that he could nothing, but if I phoned the head office they might be able to authorise a refund. At least he was honest and told me the most direct route of resolution.
So I then phoned the head office. I explained everything again (this was the 5th person I spoke to). She happenned to be 2nd in line to a manager. She was polite, apologetic and managed to get authorisation for a refund. There was a condition of course, I had to go back to the Hammersmith branch today, so I went 3 hours out of way to get there and get my money back. All in all it took half a day and visiting one branch of Carphone Warehouse, phonecalls to a government body, phonecalls to 2 different branches where I spoke to 4 different people and a call to the head office of Carphone Warehouse.
No apologies from the Hammersmith branch for miss-selling a product and telling me that the only way to get a refund is if the mobile broadband did not work in my postal address. Conselation is of course, woohoo I did get my refund back.