drain blockage an nuisance

Maintenance

Hi,
I have had a report form my letting agent that a neighbour rang about smell from a blocked drainage just outside the property.
I saw the tenant who said that when the drains were blocked she thought it was my job to clear them, in spite of not telling me of the problem, of which I only became aware because of the letting agent.
I easily cleared the drains' grate with a stick and said (rightly or wrongly) that it was her problem for discharging inappropriate stuff and showed her how to clear it.
Alas, the drain is blocked again with a little disgusting lagoon and I phoned the Council's Environmental Services hoping they would get in touch with the tenant and do something about it.
I was surprised at their response; apparently if a neighbour should complain I would also be served a notice to clear the problem.
Naturally I asked how am I supposed to force the tenant to clean the drain, apart from the fact that I did not cause the problem in the first place.
I was basically told we don't know, that's that full stop.
Any suggestions or clarifications about my position?

Many thanks