I own my own company helping LL and letting agents recover debts from tenants who don't pay, and gaining possession of property's for them from tenants who run up huuugggeeee rent bills.
In a situation where a guarantor is offered legally any missing rent or damages are recoverable from the guarantor (which is why you take one in the first place). So how finacially secure is the guarantor would be my first question.
Personally I wouldn't hold much faith in a previous LL's reference if the tenant is still living in that property. A landlord with a 'problem' tenant will be keen to help them 'move on' rather than continue to be their problem.
Have you seen bank statements and payslips? Usually give a better indication of someones finances than a credit search in a situation like this. Lots of finance payments or credit card payments with very little surplus income would suggest someone struggling. I'd also be wary of someone who drew out lots of cash to be honest unless they dont have a debit card.
I also had a CCJ that I didn't know about for a short time. It was a water rates bill for a rental property I lived in 9 years before. Knew nothing about it until it popped up on my credit file 9 years later. I eventually managed to get it taken off as it wasn't applied correctly (out of time, didn't make an effort to find new address, didn't issue correct paperwork etc etc) but it is possible he didn't know it was there.
My questions relating to the CCJ was how much was it for (something a couple of hundred quid is more likely to me a clerical error than someone forgetting to pay a couple of grand) when was it applied and what was it for.
But as I originally stated check the guarantor, make sure the letting agent knows how to draw up a watertight guarantors indemnity and ensure that if arrears/problems do arise that the guarantors are contacted immediatly. When taking a guarantor you have a duty to minimis the risk and exposure to that guarantor therefore any arrears should be notified ASAP as well as any damages and you also have to serve the correct notices at the correct times if problems occur. Make sure that the G. understands that although they may be agreeing to a 6 month tenancy that it can run on for longer as once the original 6 months is complete, the tenancy will revert to a periodic one unless either party signs a new AST or gives notice.
Most agents are pretty good at dealing with Guarantors but you would be surprised by the number that cock up appalingly and cost the LL's money.