British Brass

[Atlantia]

What a lovely example.
Although (as has been stated) these boxlock 'pocket' pistols are often thought of as lady’s carriage pistols, even sometimes generically referred to as ‘muff pistols’, they were popular with men, ’gentlemen’ and especially military officers. I agree with Fernando, this one is a mans gun, it looks very ‘navy’ officer to me.
Nelson famously carried a 'ducks foot' made by Nock.
As Rick has already infered, I would suggest that the short bayonet is to 'fix' or rather 'transfix' your target to be sure your shot is on-target.
No lady who could afford such a weapon would use it in such a way (IMHO)

Here are a couple of more standard types. The top is a Nock, the lower was made by 'Smith' of London.

I notice that your beautiful pistol also has the sliding safety catch behind the cock, I've always really liked that feature. On my Nock it engages a pin that locks the frizzen closed.