I can't tell you much about the provenance of the painting, nor especially of the chart. The chart appears to be part of a standard Admiralty Chart of the Mersey and Dee estuaries, with the Wirral Peninsula especially prominent. Such charts were standard issue aboard British warships, but were also very common aboard merchantmen worldwide.

The painting poses an interesting challenge in ship identification. It clearly depicts a WWI-era British destroyer, looking at the general design of the hull and superstructure. However, she has four funnels - most British destroyers of the period were constructed with two or three. All four funnels are of the same height, which is also unusual; typically the fore funnel was raised to keep smoke off the bridge. Also helping to narrow things down is the armament, with one gun forward, one aft, and two in tubs between the funnels. These factors lead me to identify her as a Kempenfelt-class destroyer leader. The Kempenfelt-class were constructed in the early years of WWI to act as flagships for destroyer flotillas. Next we have to identify which of these ships it is. Two of the ships, Abdiel and Gabriel, were completed as minelayers, trading in their aftmost gun for rails for laying mines. As this ship does not have these, we can conclude it must be one of the other five ships of the class. Beyond this, however, it is difficult, as we have few details, and no features such as pennant numbers that are clearly different between ships. The depiction of the ship as participating in a night action suggests that it is one of the two ships of the class that actually engaged in one. Marksman was part of the night action at Jutland, while Nimrod fought a night action against German destroyers while part of Harwich Force, on the 22nd-23rd January 1917. It seems most likely that the painting was painted by one of the ship's crew, commemorating the ship's part in the night action.