Hi Peter
My friend has an old Victorian house with original quarry tiles in his
kitchen. The tiles are about half an inch thick and he asked me if
there was an easy way to remove stains (mainly fat I think), then
re-seal them.

The problem is probably due to the very porous nature of the tiles. The
fat/grease/dirt has soaked into the tile.

The solution is not mechanical, but a hot detergent solution left to soak
for as long as possible. Any particularly bad stains, build a 'dam' around
the stain with plasticine and fill with detergent solution.

It may not come completely clean no matter what. Accept some stains as
'age' :-)

Seal using a water based acrylic floor polish. Johnsons 'Clear' is OK and
found in most supermarkets.

Dave