Rolling Lease

Tenancy Types and Management

I am a new landlord and my single property is managed by a letting / estate agent Lesley Greaves. The first 6-month lease has just finished - 25th November. I chased the agent and asked if a new lease had been initiated.
I am told by the Agent that the lease is now "A rolling contract is basically the same short-hold tenancy agreement but is on a month by month basis rather than a fixed term i.e. 6 months, 12 months. Another contract does not need to be signed/issued."
When the tenants tok on the lease, they said that they wanted security and were looking for a long term lease. A rolling contract doesn't seem to fit this need and I don't know whether is is advantageous to me either. What is your advice?