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That looks to me to be a standard door frame, no intumescent strips etc. They are not expensive. Is the quote for replacing the door as well? Its hard to see exactly what is needed from the photo you've supplied.
For reference for fitting a standard frame I would charge £80 and £80 for hanging a new door (labour only) £20 to £40 for rehanging an existing door depending on the amount of work needed. But I don't work in Brixton so couldn't help you there.
Someone kicked in my girlfriend's flat door. Locksmith said they cant do it and after having spoken to a joiner we've been quoted £250 for a new frame/materials and £250 for labour.
Does this seem legit as thought the materials seemed high. He did say they might be able to splice the wood into the side where the locks went, the door and rest of the frame is fine as it is just where the frame is made of chipboard popped.
This is Brixton Hill for reference on location