If a piece of UK land is not technically owned by anybody, can I claim ownership of it and if so how?

Answer 1

Land in the UK and in the rest of the commonwealth is always owned by someone. As a default case, that person is the Crown.

You can always attempt to buy the land from the Crown if you know who manages it.

Answer 2

If the land isn't owned by anyone, it belongs to the crown. Good luck claiming ownership. You might as well just go claim Buckingham Palace as yours.