I walked through the covered area of Kirkgate market in the centre of Leeds where fish stalls display razor clams, large conger eel, tilapia from the Indian subcontinent and turbot from the Yorkshire coast close to Todds, the pie and tripe stall which still offers maws, the lining of the sack of the pig that provides milk for its offspring (a local and definitely acquired delicacy). I went on to the outdoor area where the late afternoon bargains - one pound buys twenty five satsumas or four punnets of tomatoes – are on offer.
Here my local informant introduced me to a young couple making a good living selling mobility products to the elderly. Having teased me as to how soon I would become one of their customers, they asked where I had lunched. When I replied "Bibis" they precisely set this extraordinary thirty year old restaurant in context. "Yes, that place really is a magnet for people from all over Yorkshire when they want to have a good time."
The role of Bibis Criterion, to give it its full name, is in fact to provide a platform for anyone in fact to have a good time despite, or rather because of, its exceptional location on the ground floor of the eight storey Criterion car park. Its interior, all faux café society with palms, kilometres of chrome and an extraordinary film sequence while we were there from the less than appetising battlegrounds of the First World War, makes for an unmistakeably surreal experience.
But it has brought exceptionally success for its owners, the Teodorani family. Bibi's turnover is estimated to rival that of The Ivy in London. I spotted a female member of the family walk breezily into and out of the large open kitchen, sporting under her arm a handbag whose price tag, it was whispered to me, was a substantial four-figure sum.
The vast menu's thrust is Italian with pizzas, pastas and more. What I ate – deep fried anchovies and a huge piece of Whitby smoked haddock with spinach and a poached egg – was served with typical northern generosity. But I was surprised by a wine list which omitted to mention most of the vintages of the wines on offer, a rather offhand manner in which to treat citizens of a county whose longstanding claim to fame has been to know the precise value of everything.
By contrast, Anthony's – no more than a five minute walk away from Bibis – has already established itself as a magnet of a completely different culinary order despite having only just celebrated its first anniversary.
Anthony's is in fact the creation of two Anthony Flinns. Anthony senior has provided the finance and business acumen and was when we left after dinner 'away doing the accounts' according to his daughter the receptionist. Anthony junior is a hugely talented chef who spent two obviously inspirational summers cooking with Ferran Adria at El Bulli in Spain.
His return to his Yorkshire roots sparked the move to take over a former bar and convert it into a stylish restaurant that seats no more than 30. The ground floor bar where one can sit beforehand, order and smoke cigars afterwards is extremely comfortable while the clever design of the basement dining room precludes any thought that one is being led down to a rather inferior space.
What emerges from the kitchen is even more exciting. Flinn has not only keenly imbibed from a maestro but also appreciated his own initial limitations by opening with a small menu of four choices at each course plus of course the obligatory amuse bouches, on this occasion a small foaming cocktail of carrot, coconut, mint and rum followed by a shot glass of grape jelly topped with a cube of cod and ground hazelnuts.
My first course, a piece of home made black pudding lightened by barley came with a peppery cress salad, a skewer of salmon cheeks and mango diced into fine noodles, was sensational as was the fillet of turbot with a typical Basque accompaniment of squid stuffed with oxtail followed by an intriguing but ultimately successful pineapple and black olive Tatin. There were small quibbles: the potato base under my first and main courses were too similar; the chick peas that covered the turbot so dominant that they should have figured on the menu;and the pre-dessert of banana and hazelnut cake was perhaps slightly too heavy at that stage of the meal. But there was nothing serious enough to preclude my immediate return.
Anthony's charms rest not just with the kitchen's talents but also with its front of house team led by Olga, Anthony junior's Barcelona-born wife whom he met while she too was working at El Bulli under its exceptional restaurateur Julio Soler. She runs the room with an eye for precision and detail that many more long established restaurateurs long for, or should do anyway. Having survived a night at El Bulli when bats invaded the crowded restaurant, she seems quietly confident of handling whatever a basement in Yorkshire may offer although, perhaps not surprisingly, she did confess to still having some difficulty with the Leeds accent.
Bibis Criterion Restaurant, off Sovereign Street, Leeds LS1 4AG, 0113-243 0905. Open seven days
Anthony's, 19 Boar Lane, Leeds LS1 6EA, 0113-245 5922. Closed Sunday and Monday.