The biggest agents and landlords face with providing references is that understandably a reference has to be honest and factual.
If a Tenant is not adhering to their Tenancy Agreement, Do you give a true account of the Tenants conduct to relieve yourself open to be stuck with them and facing higher costs to get your property and costs back OR do you give a false account of the Tenants to be rid of them and move on.
Whilst I hope the former choice is adhered to I dont think this is always the case as most letting and referencing agencies only check with the current landlord, current employer/accountant and do credit checks.
I think a good solution would be to check with all previous landlords over a 5 year period or introduce a Tenant Passport which consists of a 5 year history of residential checks, emploment checks, credit history and for overseas visitors who have been here less than 5 years a comprehensive right to rent background check and mandatory requirement for a guarantor who is a UK resident meeting normal guarantor requirements and checkable background.
Thats my thought on this matter.