Jarle Hammen Knudsen wrote:
Can you recommend any heritage railways within day trip distance from
London?

I went to the Bluebell Railway last year, and it was a huge success. I
have also been on the Epping Ongar Railway.

Or anything else transport related between 8 and 19 June.

Something a little different is the miniature (mainly) steam Romney, Hythe
& Dymchurch Railway:
http://www.rhdr.org.uk

You can get there fairly easily from Ashford, about 40 mins from St
Pancras.