Before you invest a lot of effort into this plot have a chat with the committee and decide whether they are likely to support site improvement and maintenance going forward. I took on a plot in 2012 and every year the plot floods. We were led to believe 2012 was a one off so we carried on gardening, built a shed and invested time and money. We trenched the beds and the perimeter of the plot lifting the soil to raise the beds on the higher ground.
Currently we can grow non root crops on the upper third and have fruit bushes and containers on the middle third. The bottom third is dead. It is a sunny plot so we view and treat it has a garden. Our back garden is very shady so OK and we retain it for as long as no one mentions cultivation rules.
There is one plot on lower ground than me that has not been cultivated during my time on site. It is let regularly but the new tenants give up after a couple of weeks allowing the committee to relet it.
The original committee has now retired and we there is a new committee chairman who has, in the last year, allowed the site landlords onto site and I understand that they are now drawing up a drainage plan for the site. Why the landlords had nothing to do with the site before 2017 I do not know.
I could suggest if you are on a local authority site it could be worth your while contacting them to find out if they have a record of your sites drainage issues for remedial work if budgets ever allow. It is certainly worth discovering if your committee have any interest in keeping the site well maintained. If they are they will probably offer you a better located plot when one becomes available. From bitter experience I suggest it is far better to cut your losses early and get your name down on another site. Do strongly consider retaining the plot until next rent day though. It will give you time to understand the sites topography and wind patterns. Container growing can be your friend and give you opportunity to get some fruit bushes established ready to transplant into your next plot.
The ground on the neighbouring plot has flooded so much the ground level is as much has a foot lower than the surrounding paths. No dig would be the only way to go but the committee still prefers to burn the oak leaves I do not manage to squirrel away before they can get them.