I agree that a good tenant is worth a rent reduction over the hassle of a possible empty property until it is let again and the chance that the new tenants may not pay on time or keep the property in good order. But also while I agree that you have a lovely landlady, you must be also a lovely tenant that your landlady considers is worth keeping!
Regarding you needing to advise on a change in rental payments, yes you do really need to as you are possibly committing fraud by non disclosure. There is a small chance that you will get found out. If your landlady completes a tax return she will declare the reduced annual income as it will reduce her tax bill. In all probability, the authorities will not put two and two together, but this is one way that potentially you could get found out. If it is discovered that you owe money, they can go back as far as 6 years (I believe) and make you pay back the difference plus interest.
If the money that you could lose is only for a few quid or so each month, it is probably worth the peace of mind to come clean.
Anyway off my soapbox and end of lecture, glad you have got your rent reduced!