1) Crown is the Queen’s Crown so dates the cap to pre-1910 or post – 1952. That rules out the period of Edward VII and the two Georges. From what I’ve seen Victoria’s crown as an emblem was squat and flatter on the arches, but can’t see how this can be present Queen.
2) Can only be RN due to the anchor. Main shipping lines used their house emblem. Not sure about smaller owner/captained vessels.
3) The cap badge doesn’t conform to today’s code to distinguish rank. For example (and this is where it gets confusing) the Laurel sprays are used to signify an officer, but these sprays on the cap half circle rather than spread out like fingers. The rope around the anchor signifies a Petty Officer. Now here’s where I get confused Chief Petty Officers are denoted by a single wreath garland around the anchor and Warrant Officers a double wreath. (I’m not sure about Royal Marines rank insignia of this period). Up to 1870 there was no standardisation of uniform in the RN, it was up to individual captains. So that might explain the confusion. Also Officers wore formal dress uniform of tailed then later frock coats, formal headwear was the bi-corn (even in battle) and undress a peaked cap, but not this sort of peaked corded Breton cap.
4) Bearing in mind the standardisation of RN uniform in 1870 onwards, I think a date around 1850. The Crimea War was a major point in RN history from 1953-56.