Have you had to use the OpAmp offset null pins. The TI uA741 datasheet says something about using them to offset input voltage caused by unavoidable internal transistor mismatches. Maybe that causes the noisy output.
This TI application note goes into detail: "Nulling Input Offset Voltage of Operational Amplifiers"
https://www.ti.com/lit/an/sloa045/sloa045.pdf
And on page 11 of the 741 the datasheet it explains how to balance the offset with a 10K trimpot or two.
If the 741 is good for that function, great, and maybe a more application specific OpAmp would help with the objective you have, as the 741 is a general purpose device, not that it should matter.
I admit I have no idea, but maybe, or maybe not, the OpAmp is oscillating, and I remember that you can add cap + r + cap from output to input on some configuration(s), but it looks like you've done that already, unless it's a different type of OpAmp configuration.
Will that circuit transmit mains noise and 50/60Hz ripple to your measurement set-up? Does it matter or not? If it matters and it fits (safely) with the circuit function, maybe a little decoupling cap after the transformer secondary output could help, or not - you know your circuit operation parameters.