The answer of course was the railway line running from Camberley to Ascot, just up the hill from Bagshot. This cutting has an enclosed ‘tunnel’ (you can just see the entrance on the left) so that the main road can continue over the tracks.
This particular section of the line caused a great deal of trouble in the mid 19th century as the soft sandy soil was difficult to work safely. Funds ran out in 1866 and it wasn’t until 1873 that the London & South Western Railway was finished. Railway travel was, of course, already very popular and lucrative, but those wanting to visit had to go to Farnborough Station (opened, I think in 1838) and continue by horse drawn transport.
As to the answers to my three clues – I will be giving those next week!