TalkTalk provides the introduction to discounted TalkTalk deals with O2 but the contract is with O2. They can decline to give anyone credit. TalkTalk has no say in the matter but normally a good credit history with payments on time with TalkTalk would be a favourable indicator on your credit record.
Try another mobile company. You can often find handset deals that are comparable with or better than O2's.
Just remember that if you wish to keep your mobile number to get a PAC code from TalkTalk. If you get a new number from a new provider you'll need to call TalkTalk to give 30 days' notice of ceasing your TalkTalk Mobile service. I assume you're out of contract with TalkTalk i.e. just on a rolling month by month contract?
You said you'd accepted a 2GB deal from O2.
What I see is this on the O2 website - bottom left is the 3GB deal for £6.
And when I click the Buy now link I see the order:
A 1GB tariff with a 2GB free topup for 12 months. I think that is the advertised 3GB for £6 deal isn't it?
If it were me I'd make a complaint of misselling direct to O2.