Facilities

Thorpe Hall Caravan Site, in East Yorkshire has a family room, which I think has shower, loo and sink all in one. Also used as Disabled room. Another is Cliff Farm near Pickering, again, shower, loo and sink, but again considered Disability priority rather than a general use room. I doubt many CLs will have such a set up, but no doubt there will be a few.

Are you looking for any particular area Caroline? There is a marvellous CL at Pontesford near Shrewsbury which has 2 such rooms, both kept spotlessly clean. We stayed last year and had a great week. It's called Woodville CL. 

Another is Wortley Hall CL near Sheffield, not an obvious holiday spot but a great venue to stopped for a couple of nights.

But let us know where you are based or want to visit and I'm sure you'll have no shortage of suggestions.

Fishers Field in Suffolk, number 1457 in your current SD book. This is wet room with toilet

If looking for an independent site then Monks Cottage Caravan Park near Faversham in Kent will meet your requirements.

https://graham2701.wixsite.com/caravan-site

Will try to get the grey matter going over a coffee and post any others I can think of.

Radar key

Moor Edge Farm CL in Crich, Derbys has a shower facility, nicely looked after. Perhaps you can use the CL site symbols to find others? 

The affiliated site at Carbon Downs has excellent individual facilities.

Wood Farm AS near Charmouth.

Delting Marina, Brae, Shetland.

Sorry, just realised the question is about CLs.

I missed that too and the CLs do have a search facility for showers and loos ( as I checked later...)

But I think Caroline is looking for a combined shower/toilet room and it's not so easy to find those from the search function.

But, again, Caroline,  it would be easier to help if you let us know what area of the country you're planning to visit.