Contact the furniture company in the first instance. They should have a record of your payment - depending on how it was made. Was it made to the store or to their credit company? It seems odd that they haven't sent any reminders before passing it to a debt collection agency.
Don't deal with debt collection agencies by phone. They will do everything they can to wind you up and intimidate them. There is a set of guidelines that debt collection agencies are supposed to work to - but people who have dealt with them tell me that they are rude, agressive, and often tell the most blatant lies. If they call you at home, politely inform them that you will only respond to their written correspondance. They will try to argue with you, you can simply replace the receiver at this point.
Now, down to the credit reference agency. The credit agreement will have been made either with the furniture store (less likely) or with a finance company, and it will be this company that is reporting to the credit reference agency. They would have reported the debt on a monthly basis as it's status changed. During this time they would have sent reminders. Again, once your payment is proven this information can be corrected.
If you paid by cheque, you will be able to obtain a copy from your bank or building society. They will make a small charge (it will be under £20) for this. Likewise, you can receive copies of transaction slips if you paid by card (even over the phone). Bank and especially ex-building society staff (bless em) often don't know this, so push if necessary. Get them to contact their head office for instructions.
If all else fails challenge them to provide written proof to substantiate the debt. If they can't, they will not be able to enforce anything in court. Speak to your local citizen's advice bureau should this happen, refer to the excellent http://www.consumeractiongroup.co.uk/ for sample letters and some great advice.
Lastly, for the record, this sort of default would not exclude you from a career in the police. What they are looking for is evidence that you are over-extended or have a compulsive behaviour (such as gambling) which could potentially make you more liable to succumb to financial inducement; this is from police recruitment:
5.7 As individuals are most vulnerable when they have large debts that they cannot sustain, the purpose of financial enquiries is to ensure they have direct or indirect access to sufficient funds to minimise the risk of vulnerability to financial inducement. Where anomalies are noted between their financial declaration and the information provided by the credit reference check, or where there is a need to seek clarification, the RVTL will consult with the applicant.
Of course, the debt collection agency would be pleased to reinforce the mis-conception. They would tell you the sky will fall in if they thought it would make you cough up. Don't just tell them you're going to speak to citizen's advice, go and speak to these people.
Deal with them only in writing, keep copies, send recorded delivery. Obtain proof of payment from the store, the finance company or your bank. Do not be intimidated by the debt collection agency. Do not ignore it, they are persistent.
