Hello James,
I am sure it is possible to build your own caravan, but despite the freedoms our forefathers fought to maintain, there are regulations you must comply with
Firstly let me deal with the aspect of which I am absolutely sure, the gas system. I am sorry James but contrary to Mike's contribution, the law now requires that all fitting servicing repairs and removal of any fixed installation to be carried out by a competent person who must work to the current set of Gas regulations. Unless you are trained in LPG installation, it is very unlikely that you will have the necessary knowledge, and test equipment to comply. failure to comply is breach of health and safety regulations, and it applies to ALL gas installations, even those on self build caravans.
Electrical systems are slightly different, you can DIY work on some systems, but it must be certified by an electrician before it is connected to a mains supply.
The trailer must comply with the road vehicle regulations as far as weight, lights and brakes are concerned. If it is a modern chassis, it will already be plated with the maximum axle load, and you must not exceed that limit.
As for the construction, you must bear in mind the max width the law allows, but apart from that you technically have free reign on the design you come up with. the only other things you will need to be aware of, are the amount and placement of fixed ventilation, and how to maintain the caravans structural integrity when all the forces or towing are in play. Get it wrong, and the trailer may be deemed an unsafe vehicle if spotted behaving badly.
You may have trouble getting insurance, as most companies use lists of manufactured caravans. And of course it will not be covered by the NCC design approval scheme. This does not make it illegal, just difficult to sell on.
best of luck