I'm 85 years old and would loe to visit Burnham and the coast line. Is there a railway station.
The nearest railway station is Kings Lynn, from there the Coastliner bus 36 operates hourly to destinations along the North Norfolk Coast.
King’s Lynn railway station as mentioned - there’s then the Coastliner 36 bus from the bus station about 5 to 10 mins walk away
https://scenicbuses.uk/routes/lynx-coastliner-36/
https://www.lynxbus.co.uk/bus-routes/coastliner-36/
One could also get buses (Coast Hopper then Coastliner) from Sheringham railway station depending where you’re travelling from.
Including the Coasthopper between Cromer and Wells (you can get a train from Norwich, to Cromer, West Runton and Sheringham) https://lovenorfolk.co.uk/norfolk-coastliner-coasthopper/
You need to be a little careful. Depending upon how you count them, there up to 7 Burnhams within about 2 miles of each other. The main village is Burnham Market. It is about 2 miles inland. The bus will drop you off in the middle of the village. Burnham Deepdale and Burnham Overy Staithe, both on the coast, are also on the bus route. Nelson's birthplace is in Burnham Thorpe bus there is not a bus service to this village. I'm sure Burnham Market is the place you want.