...You are a serious enthusiast photographer and you would like to make some money from your photography, so you have a website where you offer your images for sale (zenfolio/smugmug/personal/etc). Are there any public spaces in the UK where this would be restricted?
The answer depends on three things (all of which have been mentioned earlier)
1) What you define as 'public space'
There are a significant number of areas which the public can freely enter, and which are not obviously different to a publicly owned open space, but are actually privately owned.
If it is genuinely a publicly owned space, then in general you are free to take photographs and sell them if you choose (subject to 2 & 3 below).
If it is privately owned land with general public access, then it's up to the owners of the land to decide what is, and is not, permitted. Which is the main point of this thread - often an area which appears public is in fact private, and restrictions on photography can apply (and may well only be obvious when someone shouts at you to stop!)
2) When are you taking the photographs?
Sometimes publicly owned land is used as the site for an event - when this occurs, there are often restrictions on photography, but these are usually fairly obvious (though sometimes badly defined, EG 'No Professional Cameras').
3) What / How are you taking photographs?
Most photography is fine, but there are exceptions - being on public land does not mean you can use a long lens to see into a space where someone might expect degree of privacy, there are also some military / security areas where you are not permitted to photograph them.
There are also cases where photography is OK, but the way you are doing it means you will be asked to stop - setting up a complex lighting rig that blocks a busy street, for example, will probably end up with you getting told to move!