Different but somewhat related story. Some time before the first world war – someone else look it up, please – there was a reform of German coinage. At the time, one mark (Reichsmark then) was worth 1/20 £ (suppose both were tied to silver so the rate was fixed?), and accordingly size and diameter were matched to the British shilling.
This specification of the mark piece survived all the way to 2001. Both world wars and re-unification. It survived the currency reform after hyper-inflation in 1923. The post-war reform in 1948. The design changed so many times and the alloy, too – but diameter and size were unchanged, and the same held true for shilling/5p in the UK till the 5p became smaller in 1990.
The exchange rate, however, changed massively in favour of DM. Hence, my uncles, whenever travelling to the UK, would collect as many 5p as possible and carry a huge jar home – these coins would be accepted by most cigarette machines. For 1DM you'd get six or seven 5p pieces.