A new high-resolution tunable RF/microwave photonic notch filter with low-noise performance is presented. It is based on using a dual-input electro-optic intensity modulator together with a frequency-shifting amplified recirculating delay line loop. It can realize a very narrow notch, and also a wide and flat passband to simultaneously excise interference with minimal impact on the wanted signal. The notch filter can be integrated into optical fibre microwave transmission systems. Experimental results are presented which demonstrate a notch filter response with a very narrow notch width of 0.55% of the filter free spectral range, a wide and flat passband, and a high signal-to-noise ratio of 114 dB/Hz. The ability to tune the notch frequency of the filter is also demonstrated.