Mainline trains run from London Kings Cross to Berwick upon Tweed.   If travelling from London or the south, recommend a night in Edinburgh and then travel to Melrose the next day to break up the journey. From here you need to catch the bus to Melrose.  At the end of the walk from Holy Island catch a taxi to Berwick to connect to mainline rail services. From Bamburgh or Craster, catch a taxi to Alnmouth for trains to major cities. Refer to www.nationalrail.co.uk and www.perrymansbuses.co.uk