Fake as in newer. She said it still has historical value. I not sure what value is!
Well for me this is more than a hobby - i've been working at auction houses for 13 years - and something like this is quite tricky. Were this just a c1900 mug by an unknown or uncelebrated potter with that message on the side, i think it would be estimated at £60-100 or £80-120 - classic auction house estimates for items that can go either way.
However, the provenance here is very interesting, even if ultimately unproveable. I think it's worth more than that and i would be researching the residents at the relevant places - it's not information that will be readily available on the internet. There's a paragraph on that page which mentions a few names but little background.
I'd be in a library or museum researching this.
Even if not as old as we hope, if it originated from that street then it's a wonderful thing.