Woody Bay is a terminus on the Ruislip Lido Railway line. It is run by volunteers so tends to operate when there is likely to be demand, for example on summer weekends (timetable here), but there are other things to do at the Lido which is well worth a visit in its own right - and it offers free parking and free admission (although you will pay to ride on the train).
The railway runs through woodland around the lake on a (very) narrow gauge track normally pulled by a diesel engine, but on summer Sundays they often bring out a steam engine to pull the train. I have fond childhood memories of being taken on the train by my parents and grandparents, and I have taken my kids/grandkids on it.
The cache is a magnetic micro containing logbook and pencil only. You will not need to pay to go on the train as this is in a public area.
Watch out for muggles - it can get quite busy here! Originally the cache was magnetically stuck to the track in the siding under the buffer (literally sidetracked), but repeated muggling meant that I had to move it a short distance to the location indicated by the above coords. Probably a good job as the track has now been taken up.