Yup, you can refuse to pay a civil-issued fine. There is nothing in law that can be done against you beyond their own powers to put your vehicle “outside of your use”.
There IS however plenty OUTSIDE the law that can be done against you - should you find yourself still on or later returning to the issuer’s property.
(1) They can clamp you. The police won’t get involved in taking the clamp off, so you have the choice of either paying the huge fine and extras added on, or taking it up with the clamper. 
(2) The clamper will of course not be present 99 times out of 100, as they are scared children afraid of confrontations, and lie in wait in the bushes until the vehicle is absolutely left alone before proceeding. Once the clamp is on, they scarper fast, your vehicle always strangely being the ONLY one being clamped in the area… (Clamping a whole series of vehicles leaves them open to being approached by disgruntled drivers, thus they do a one-off and leave the scene!) 
(3) You can approach the MSA management, and they’ll just refer you to someone who’s not present. They’ll no doubt take your money if you offer to pay the “fine” though. Most people don’t make this mistake, when it becomes apparent that paying the fine doesn’t actually get the clamp removed - because the clamper isn’t present! You’ll find this out first, then refuse to part with any cash until you have someone present to rip the head off of, and crap down the hole. 
(4) since (2) is no different from someone actually breaking into, and stealing valuables from your vehicle, in law there is no difference to the response. The police will never go any further than give you a crime number. Possession is 9/10ths of the law, and your vehicle being clamped, and the person with the ability to remove it not being present, you are up crap creek without a paddle. 
(5) If you are able to leave the scene, and a fine comes in the post, then you can choose not to pay it, but must consider yourself “banned from site” in that you’ll be clamped for sure at ANY MSA around the country should your vehicle be recognised by the auto-recognition system. Breaks every law in the book, but our lawmasters and enforcers are owned by the crooks, so you won’t get anywhere on the “public power” front unfortunately. 
(6) Invite the clamping firm to attend your property to receive your cash payment as you have no bank account, and then clamp them with the arbitary fine of £1000 cash per day or part thereof. They’ll send someone around with bolt cutters or whatever to remove it, and you then can involve the police for breaking and entering AND going equipped for burlary!

Of course they’ll never agree to come around your place in the first instance, but this knowledge also extends to the interesting fact that debt collectors won’t bother comeing around either!
(Periodic dirty letters, threats of bankruptcy or further court action, or even a letter that LOOKS like it’s from the court - but no actual person in a suit turning up on your doorstep, as has been the way for debt firms for nearly 10 years now!)
I would be interested to hear from anyone who’s successfully bolt-cut a clamp off, and the aftermath… I would imagine that the brudders have already been doing this for years, and they don’t have a great reputation for paying their fines do they?
People sitting in their vehicles don’t get clamped. so Don’t leave your vehicle unattended at MSA’s therefore HAS to be the moral to this story in conclusion then! 