The shop's not much to look at, but along with the corner house this dates from circa 1835-44 and is Grade-II listed.
The Post Office Directory of 1898 lists it as a chandler's shop run by a Mrs Amelia Bowerbank. I had a look through some earlier directories, but as the listings weren't by street I couldn't find anything for it ... so that's pretty much all I know.
Architecturally, it's a wooden shopfront with pilasters, entablature (although with some rectangular panels attached) and bracketed cornice, but there's nothing fancy.
Swinton Street's first houses were built in 1776, and it was originally a small cul-de-sac. The first occupant was able to gaze across the meadows to Fleet Brook. The western end of the street dates from that period, but the later houses that extended eastwards, including number 35, were begun in the late 1830s and completed by 1844.
And the street has pretty much remained the same since, despite major developments in the nearby area, notably the building of the railways and King's Cross station. I had a look around to see if I could find any old images of Swinton Street and the best I could do was this from a London Illustrated News of 1862, which shows the construction of the first section of the Metropolitan tube line, between Paddington and Farringdon. A small section of Swinton Street can be seen jutting out to the left behind the front-facing building just left of centre. The few houses furthest away are Britannia Street.