Barclays Internal Scoring

Frankel

I am 23 earning 24K a year and currently have access to the following...

MBNA Credit Card (£900 outstanding / £3000 Limit)
Natwest Credit Card (£1500 outstanding / £3000 Limit)
Barclays Platinum Credit Card (ZERO outstanding / £2000 Limit)
Barclays Credit Card (ZERO outstanding / £250 Limit)
2 x Barclays current accounts - both out of overdrafts

I have also just paid off a £5000 Barclays loan.

My credit score is not great due to some late payments back in 2008 with 02 (which I am disputing)

However, my Barclays Credit History is good.

Am I likely to be viewed as a good fit for another Barclays Loan when I apply next month? (5K)

NeverEnough

No-one can give you a definitive answer except Barclays themselves, but given that if successful, your credit limit will be more than 50% of your income it is unlikely that you'll get a 5K loan, particularly if there are adverse issues on your credit report, even if you are disputing them.....
5K loans are not as easy to get now as they were a few years ago, and Barclays don't just look at your internal history with them, they definitely check the CRAs, I think Equifax is the one they use.