Brockley will be connected with Crossrail via a brand new interchange at Whitechapel, to which we're directly connected by the East London Line.
The new station looks absolutely fantastic and will also improve the interchange with the District Line.
When completed, Crossrail will provide Brockley residents with better routes to destinations like Tottenham Court Road, Paddington and Heathrow. It will also support the long-term growth of Canary Wharf and continue to drag London's economic and cultural gravity eastwards, which is why people like Simon Jenkins hate it - they'd rather spend the money improving existing infrastructure for the parts of London already well-served by public transport, rather than creating new capacity to spread London's growth. Fortunately, they seem to have lost the argument.