Hi Can anyone recommend methods or products to clean and

Apparently, a mixture of flour and hydrogen peroxide,  applied as a paste and allowed to dry does work - but never tried it myself

Thanks Alan.  That's not something I've ever used before but sounds interesting. We're replacing the old windows and so wanted to have a go at cleaning the windowsills first.  

If you do manage to clean them up,  I'd suggest sealing them with s limestone floor tile sealer