But merely because the fleet is meagre - just 10 or 12 boats 50ft to 60ft long with crews of five or six - does not prevent the hopes of the British fishing industry riding on its growing success.
British tuna fishing is in only its third season, the result of diversification as quotas of traditional white fish have been cut annually to protect dwindling stocks and profit margins have come under pressure.
The uphill task facing those who market the oily fish - mainly the albacore variety - is persuading the consumer or restaurateur to try it.
It is a problem accentuated by the fact that tuna is only available from mid- June until September when the fish migrate through international waters in the Bay of Biscay.
Godfrey Adams, of Trelawney Fish, in Newlyn, said: 'You can't get your teeth into it because it's not all year round.'
However, of the 300 tons of tuna landed last year, the vast majority of it at Newlyn, about a quarter was sold for consumption in the domestic market.
The rest was sold across Europe, mostly back to Spain where buyers are used to the light-coloured flesh of the albacore, as opposed to the darker hue of the yellow fin.
The market for the fresh albacore in Britain has been increasing gradually. However, most sales are of yellow fin, blue fin and big eye varieties, imported fresh or frozen.
Yesterday, Trelawney Fish was buying albacore wholesale at between pounds 9 and pounds 11 a stone (6.3kgs), all of which will be sold fresh. Mr Adams said that merchants were not interested in selling fish for canning as the prices paid were too low.
'Merchants are also keen to develop the market here and so are looking for the best fish and the best prices,' he said.
'It's very easy bunging all the tuna into a lorry and sending it off to Spain for canning. But if you look after it a bit better, grade and pack it in polystyrene boxes in ice, you can sell it fresh.'