Club trade in advice | Golf Monthly
For irons, you could go for something like Benross, which you can get for about £200, I think you would notice a huge difference in distance gain and accuracy with these and wouldn't blow your budget. I do remember reading that if you want custom fit they won't price match so keep that in mind.
Have a look on their website and see what fits in your budget as if it is on their website you can get them to order it in. If not, it is what is in store. For example, my store has a few clubs available which are not on their website anymore.
And you are correct about the wedges, it is 1 for 1, so most likely not worth trading in for.
For the putter, you could easily pick something up for your budget but it is really up to you what you want to go for. You can go in and try a few and see if you can find one second hand for cheap.
My advice would be to go for irons as I do think you'd notice a big difference, and there is cheaper brands out there which still perform great.