Hi. Depending on the size of your extension you might need planning consent, and in any case you will need Building regs approvals. Assuming you're using an architect then they will probably have a 'cad monkey' to prep the plans for you. Ask for an all in fee quote from the start. There's tons of CAD plan providers about, so if your not using an architect just phone up for quotes from a few firms and tell them what you want. I think I just paid £400 plus vat for full sets for NHS planning app for a small building, so that would have been a gilt edged fee from some fancy firm.
How long is a piece of string? Depends what you want, how much input you need (plan draftsman or architect), do you have current plans or do you need a survey, is your proposal straightforward or more complicated? Do you want planning drawing or building regs as well? Do you have a one bedroom house or something much bigger? It could range from around £500 to thousands & thousands of pounds?
I don't know, but when someone with more knowledge comes along they'll probably be able to give a more accurate answer if you give them a clue what the extension is like -- plans for a three-storey extension with new bedrooms, a bathroom and a massive kitchen will cost more than plans for a single storey extra bit of living space.