The terms of any contract which exist between you and your former tenant can't modify the terms of the contracts which existed between him and the utility companies. His contracts with them stated that he'd pay the bills during the time which he occupied the premises and that the contracts would come to an end when he notified those companies that he'd vacated the premises. Thereafter it's up to you, as the landlord, to either pay the bills or to suspend the supply of the relevant services which bring about those bills.
The utility companies have every right to pursue you for payment, through the courts if necessary. A few red bills will probably have little, if any, significant effect on your credit rating (as long as you pay quickly). However further delay in paying them (particularly if the utility companies seeks CCJs against you) will have a severely detrimental effect. It could then take several years to re-establish a decent credit score.
As stated above, your contract with your former tenant is irrelevant to the utility companies. They can (and almost certainly will) continue to seek payment from you. It's then up to you to chase your former tenant for the money you've had to pay out as a result of him failing to meet the terms of his contract with you.
Chris