Police say I must extend my T1 1 month before it expires

The other day I went to police station to change my address because I need to register with the police. I was surprisingly told that I must extend my tier 1 visa at least one month before it expires. I think somewhere I've seen that as long as I send out my application before the last date of my visa, that will be fine. But I was shown some printed paper and it says "must" rather than "recommend". So it seems pretty official. Anyone know the rules? Any quotation from the rules would be very helful.

The immigration rules (245C) do not seem to require that you have to extend a month before your leave expires.

Although they encourage you to apply one month before your leave runs out, 245C seems to permit a leave to remain application even if your leave had expired. However, you should apply before your leave expires because if you are refused and have no leave remaining, then you should have the right of appeal. If your leave expires while your valid in-time application is being considered, then section 3C will come into play.

See also Points Based System appeal succeeds.