Dunno whereabouts in NW Kent you are, but if you can get to Gatwick or Croydon, then Southern Trains are running a skeleton Brighton-Gatwick-Victoria service along with half-hourly services between both East & West Croydon & Victoria, there's a car park next to West Croydon station.
Should TFL/RMT remember what 'public service' means & decide to run on Boxing day, & you can get a lift to West Croydon then your best bet may be to get the East London overground from there directly to Highbury & Islington.
If the Croydon Tram service is running, then you could maybe catch that at Beckenham Junction to West Croydon.