Right - I have a sort of answer. Bought this diamond coated cutter from
Screwfix:-

http://www.screwfix.com/prods/87575/Drill-Bits/Tile-Drills/Diamond-Core-Drill-6mm

And it's not exactly fast but worked. You need to get a centre first for
it - I used a multi-purpose drill bit for this, or one of those flat head
tile drills would probably work too. I used a slow speed - about 200 rpm -
and dipped it in water frequently. Took about 5 minutes for a 6mm hole in
7mm thick tiles.

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*I speak fluent patriarchy but it's not my mother tongue

Dave Plowman London SW
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