Hi and welcome to the world of agricultural volunteering! I'm not the best ambassador- I have not officially wwoofed! I have volunteered/interned on farms that had wwoofers, and participated in Turkey's equivalent of wwoof (bugday-tatuta, if you ever go there).
I'm a single, so not the most relevant to your concerns about couple-dom. I can say that where I've worked when a couple has come in they knew ahead of time whether they were going to get private accommodations or not. Most hosts will be clear with you prior to arrival about your sleeping situation. Regarding whether or not you provide the caravan, I assume if they offer for you to stay in a caravan they are offering the use of their caravan, unless they say they are providing a site with hookups for any interested, then it is probably not provided.
Most hosts give access to laundry facilities- I've even had a host or two that did my laundry for me, though it was certainly unexpected and not the norm

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If you are hoping to save money hitchhiking is very cheap. I know buses and trains in the UK are pricey- I was there two years ago. I decided to take the bus system. They have a neat discount card you can buy and save ~10% on each trip. Even though I only rode the bus three times, signing up for the membership was worthwhile and saved me 20-30 pounds. As a couple, you are one of the safest hitch hiking combos- I recommend it! If you want a fun way to stay in a city (or perhaps rural if you luck out) overnight (or a few nights) try couchsurfing.org. I don't know if travel companies are the same in the UK as the U.S. but it is worth getting travel tickets well ahead of time if you are able to line up farm gigs far in advance. Sometimes it doesn't work out in the wwoofing line of work

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If you are worried about what to bring, I recommend asking your hosts if you need your own wellies, work gloves, hat, sunscreen if you use that, toiletries, etc. I traveled with (and still use when traveling) a thin towel made out of a material that dries within thirty minutes- excellent if you want to take a shower early in the morning before departing to a new locale- my mother taught me you can only make a first impression once

. Lastly, some enjoy having a notebook with a pen or pencil to record bits of information gleaned during your stays (references, ideas, journal, contact info).
Also, helpx.net is available. It is not solely agricultural, nor always organic. Another viable avenue.
I hope you enjoy your working together! I find traveling around and working with various homesteads and communities quite enjoyable.