http://www.ukcampsite.co.uk/ is a good place to find campsites. If arriving at a Camping and Caravan Club site, book in as a non-member 'backpacker' for a decent price, often below that charged by sites set up for tin boxes!
On android it is an indirect link via google - ditto W10 - coming up France last autumn i found many campsite didnt have websites - considering it is compiled by a retired dutch schoolteacher it is still not badArchies app seems good so far. Would have been useful to have a link to the campsites' websites though.
... but their insurance may not allow it..... there's always somewhere for a 1 man tent.
Camping & Caravanning Club sites will always find room for a cycle camper - even if they're full. It's actually part of their rules.
I'd recommend joining the C&CC. It's relatively cheap and helps support a really good network of campsites and certificated sites.