Is there anything that can be done to stop cyclists riding on the pavements in Brighton & Hove?

My friend was having a meal at the Melrose Fish Restaurant one evening. A cyclist was riding along the pavement looking behind him at something that had caught his eye - not looking where he was going - and knocked down an old lady who was visiting Brighton and out for an evening stroll.

I have seen near misses so many times. Is there nothing that can be done to prevent this? Maybe a campaign between Brighton and Hove City Council, The Argus and Sussex police?

-Pauline Sloan, Brighton