Thanks for your reply. I've just remembered that many, many years ago I stayed (with a school cricket team) at the YHA hostel in Sheringham. I've just checked it out and there are a few isolated (non-consecutive) dates available in the near future at £13 per night (or £10 per night if you buy a year's YHA membership).
That, in itself, might not help you much but it spurred me into looking at other coastal YHA hostels. Littlehampton, for example, has some beds available from next Sunday (18th) through to the following Thursday (22nd) at £13 per night (or £10 per night if you join the YHA).
Start here
http://www.yha.org.uk/
Click 'Places to Stay' and then a region which interests you.
From there, click on any coastal hostel which might be of interest.
Then click 'Check Availability'.
Doing exactly that has just led me to the Berwick hostel which has several consecutive nights in the near future available at just £11 per night (or £8 per night for members).
Happy hunting!