We are building a double storey extension to the back and side of our house. Can anyone tell me if it is cheaper to build in block work and then render or build with bricks? (The existing house is brickwork that has been fully painted White so we would potentially need to render the whole house) Thanks

999 out of a 1000, if i was given the choice - show brickwork every time.

Render is a pain, plus it is a long term maintenance issue.

Build costs are marginally different if anything, but then render is an ongoing cost and risk, which is not present with brickwork

Planning conditions would normally require the extension to match the house, but that would not mean painting brickwork or rendering. If the house is brickwork, then build in brickwork and leave it unpainted

Fully support noseall and woody. My take on this is: never paint brick or stonework. Painted render can cause all kinds of difficulties, not least, condensation - even with "approved" paint.
If you were to attempt to render over the in-situ painted brickwork you would first have to grind off the paint - lots of work esp. at the reveals and details.
FWIW: the painting of brickwork Victorian and Edwardian terrace houses over the past 40 years has resulted in slumlike eyesores, and the mutilation of what should be national treasures. Go to Bradford, Oldham, and Longsight Manchester and weep.