It happens that Jonathan formulated :
Do I: Drive all the way to B&Q and see if there is some super drill bit for
ridiculously tough concrete (is there?) , OR, use a good splurge of "no
nails" to glue a square of wood into the wall, and then drill into that?

You need to look up an SDS drill and bit. Expensive for a single use
though, but it is the only way. 'No Nails' will certainly _not_ support
that kind of weight - fine for holding the wood batten alone, but not
for anything attached to the batten.

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Regards,
Harry (M1BYT) (L)
http://www.ukradioamateur.co.uk