Probably not so likely.

The portion of the population most likely to have a tattoo in 1850 would have been seafaring men.

Tattoos had not spread far beyond the seafaring population until later than 1850.

The population of seafarers and ex-seafarers in Britain is estimated at 600,000 (the number of sailors employed in the merchant marine was 178,000 at this date - add in the Royal Navy and retired or former seafarers to estimate 600,000).

The total population of Britain in 1850 was 27.5 milion.

Seafarers made up circa 2% of the population.

Not all seafarers would have had tattoos. (Say less than half?)

Unless you live in a seaport, or have a very wide circle of people you "know" (perhaps 1 in every 100 people might have a tattoo in the overall population), you probably don't know someone with a tattoo. (Though you would be more likely to have seen someone with a tattoo. (The coverage of the clothing worn in Britain, and the often chilly climate, however, might mean that you might well not know that some of the people you saw, or even some of the people you knew, had tattoos.)