Good bastards @Tommy and @Glycerine gave me a collection of reloading gear, including a Lee press.
As I was mounting it to the bench, I noticed one corner of the base was broken off, right through one of the three mounting holes. I mounted it anyway, and had a go at depriming/sizing a few cases, and the press was flaccid as. This would not do.
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I hatched a plan to repair the damage and reinforce the base using materials I had on hand (helps to have a decent set of facilities at work too).
I wish I took more photos of the process, but in short, I used Devcon (aluminium filled epoxy) to glue the broken corner back on, then once that had cured, used more Devcon to bond the press to a piece of 8mm Aluminium diamond plate, with countersunk bolts up through the existing mounting holes in the press.
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All that's left to do is drill new mounting holes in the corners of the diamond plate and mount the thing. Should be sturdy as.