We made another attempt at finding an apartment today, and this time the estate agent was open. Unfortunately our tourists' guide book doesn't include phrases useful for finding long term accomodation, but thankfully the agent spoke German so we could manage a little, and she called someone else who spoke English to help with the finer points. Now this may come as a complete shock to us foreigners, but apparently over here seaside apartments have a fair bit of demand over the summer, which can lead to an inflated price. Apartments around here are very much out of our league.
It doesn't help that the cheapest places are in rural areas, and the estate agents are in the cities, and the estate agents don't tend to cover more than the city they are in. In fact finding any lettings here is very hard, and our being fussy about not spending an absolute fortune just compounds the issue. So although we can afford to live here, it looks like we would have to buy a house to do so.
What we have found is a room for rent where the host will kindly let us use their kitchen. It is a few miles south from the coast, with a nice garden leading down to a large lake. Use of a kitchen is going to be necessary as the room costs £10 a night so we won't have much money left over for food - not that it is a huge problem if we go over budget by a pound or two every day.
So we should have a very pleasant summer to look forward to, being not too far from a national park, the sea side and a good bakery. We are also within easy cycling distance from Germany in case we need to go and get decent ice cream.