there's no strike tomorrow, but RMT and ASLEF members are operating an overtime ban. have a look here:-
http://www.southernrailway.com/your-journey/strike/travel-advice-for-aslef-overtime-ban/
on the accompanying map, Crawley is "brown", ie reduced service - check the website before you travel to see what southern services are running; alternatively take a thameslink train from St Paul's, Blackfriars or London Bridge to Three Bridges, then "cab" it from there.