I have designed which I believe is a novel method in the form of a product for an existing process (i.e. from all my research and patent searching I see no one else doing the same). I understand that I can apply for a provision patent application while exploring the commercial value of the idea;
I assume you want to write this application on your own and maybe consult an attorney for the non provisional application. While this is a common strategy and it is true that the non provisional can have more information to fix mistakes in the provisional or add other specifics, I would like to emphasize that every mistake made in the provisional application can lead to losing the filing date of the provisional application.
This means that if you (or any one else) disclose anything which might render your invention not patentable (due to it beeing not novel or not inventive anymore), you cannot correct any mistakes anymore and you could easily be stuck with a pretty much worthles patent application. I know the pro's of this decision, but you should also understand the problems with doing this on your own.
Now, back to your question:
If I submitted for the provisional patent application - protecting my idea for 12 months, and deliberately don't apply for a full patent (due to it be extortionately expensive for starting inventors). Will someone else be able to carry on where I left off and patent the idea,
In principle, yes. For more information see my question here. But you have already mentioned the solution:
or is it the case that in those 12 months if I publically disclose the idea and commercialise it that it will be a free-for-all and I can rely of my reputation to carry forward?
If you publicly disclose your invention, it counts as prior art for every patent application around the world (or at least in almost every country, there might be a few where this part of the law differs, I don't know of any though) filed after the disclosure. That means, nobody should be able to get a patent on that invention anymore, if they file the application after your disclosure.
This kind of defensive publication should be made in written form, somewhere publicly accessible and with as much information as possible to be a good prior art document. The date of publication should be visible and provable.
This does have the drawback that you are also creating prior art for your non provisional application (thats what you called "full patent" application), so everything you left out of your provisional, formulated in the wrong patent language style or simply missed cannot be protected anymore.
It also constitutes prior art for minor improvements you might come up with in the time between the filing of the provisional and the non provisional, which is the reason peple don't run around talking about their still unpublished patent applications most of the time.
I don't know exactly which fees have to be paid at the filing but I think the fees that are so "extortionat" can be delayed for the first year while you make your decision, so you can use a normal application the same way as a provisional application (you have to check for the UK, but Germany for example allows most fees to be paid later (or not at all if the application is abandoned later)). This way you have your defensive publication without it beeing published. And as you - and only you - can claim priority to the first application, it won't be in your way.
But as a protection against others, it does work. There is another way though.
I'm not 100% certain about the UK so the next explanation will be about EP patents and if applicable you can just do the same with UK patents, if not, go to the UK through the EP application.
An EP application may claim priority to another EP or national application for one year. An EP patent application is always published after 18 months and then counts as prior art regarding novelty (EP + US) and inventiveness (US) dated backwards to the day of filing.
To be clear, it is published later but counts as prior art from the day of filing!
The same goes for most national applications in europe, so if you file any kind of patent application which is inherently published after some time, this will prevent anyone from getting a patent for the same invention filed afterwards and in the US it will even prevent similar patents (which are obvious in light of your invention).
And while for Europe you only have protection regarding novelty of other patent applications (= others cannot patent the same invention after you), for the US cou are protected against someone else filing an obvious imporvement too. So for the US , this will protect you in the same way as a normal publication would - just with less drawbacks.