Firstly if you find a piece of land you need to make sure that it is in the development boundry. If not you have very little chance of getting planning permission for a dwelling(unless you have a big backhander wad in your back pocket), the plans with the development boundries are available from the planning department of your local authority, (to look at there and not take away), or most local authorities have them online these days. I would think that a park would almost certainly be outside the development zone. Once you have found your plot, some planning departments will visit site and advise, others won't. The local elected member (councillor) for the area where the plot is situated should be able to help and also any elected member on the planning commitee should also be able to help.
Plots are rare and expensive, look for houses with wide frontages that you could build in the garden, or so run down that they need to be knocked down and rebuilt.
I think that you can apply for planning permission on any land anywhere, ownership does not come into it, the value of any land will go up if it has got permission so if you find something, apply for planning and get it before the sale is complete you may find that the owner withdraws, try for an arrangement where it is agreed that you will buy and complete as soon as planning permission is granted.