After relocating to Mayfair in February 1997, The Square won a second Michelin star in 1998, which it retained until 2016, the same year when Howard and Platts-Martin sold the restaurant to a company held by Marlon Abela.

Former Oxford-educated lawyer Nigel Platts-Martin and chef Marco Pierre White, co-owners of Harveys, planned to establish a second restaurant in West End.

[2][9] A restaurant critic Jonathan Meades in June 1992, described the original St James's location as "big, spacious, quirky" and its interior design as "pretty startling and very boldly coloured" with "[a] giantess's ear-ring hang[ing] [at a] window" and multiple gold leaf decorations.

[11] The New York Times food critic Catharine Reynolds in November 1995 wrote, "The dining room is screened from the street by variegated ivy topiary and dangling metal spirals charitably described as gypsy earrings gone wrong".

In November 1995, The Square served eight first course dishes, including "seared tuna with a tartare of vegetables and soy-wilted greens and a warm salad of gam[é] and chestnuts".

[16] After multimillion-pound Mayfair eateries Sexy Fish and Park Chinois opened in 2015, rents and premium rates increased for offices and other restaurants around the area, including The Square and Hibiscus.

[5][19] Howard, later in 2016 opened a new restaurant Elystan Street, where the menu is less complex than The Square's, with his business partner Rebecca Mascarenhas.

[22][23] The Square offered seasonal (monthly or otherwise) menus, which it had been originally doing since its opening in St James's, set at a single price.

Starter course choices for the two-course meal included "roast foie gras with caramelised endive and muscat grapes" and "a sauté of scallops and langoustines with chanterelles".

Main course choices for the two-course included "herb-crusted saddle of lamb with white-bean puree and garlic" and "roast Bresse pigeon with a tarragon mousseline and foie gras".

Among the first-course choices were "seasoned scallop-mussel soup" ("nage", according to the menu) "with white wine", and a "bresaola (dried beef), with a salad of haricot verts, favas, tomatoes and potatoes".

Among desserts were an "apricot-almond tart" and "a shortbread sandwich filled with strawberries and crème fraîche [served] with vanilla ice cream".

Among dishes served from the menu were "a tartare of line-caught mackerel with young beetroot and sour cream" also containing oysterleaf; a "steamed fillet of day boat turbot with Japanese mushrooms, smoked razor clams and kombu dashi" incorporated with "seaweed, white soy and katsuobushi (dried bonito flakes)"; "a warm velouté of Lincolnshire smoked eel with Jersey Royals, apple, leek hearts and oscietra caviar", which used curry leaves for seasoning rather than salt; "lasagne of Dorset crab with a cappuccino of shellfish and Champagne foam"; "tartare of milk-fed veal with burratina [sic], white peach, artichoke and fennel"; a "roast fillet of line-caught sea bass with barbecued smoked eel, Savoy cabbage, hand-cut macaroni and red wine"; a "roast rib of dry-aged beef with caramelised onion, parsley and garlic purée, duxelles of girolles and red wine"; "Scottish raspberry soufflé with lemon verbena and raspberry ripple ice-cream"; and "Dorset blackcurrants with hibiscus and sour cream".

[11][28] In February 2013, Weston left The Square to become the head chef of Chiswick restaurant La Trompette, owned by Nigel Platts-Martin and Bruce Poole, which was reopened later after refurbishment.

[28][29] Australian chef Josh Pelham worked previously as a sous-chef of Kitchen W8, one of the restaurants owned by Phil Howard, which earned its first Michelin star in 2011.

[46][47] James Villas of Town & Country in June 1996 praised "Howard's brilliant, highly personal approach to modern British cookery" that had resulted in "intelligent, well-balanced" dishes.

[48] The Times restaurant critic Sheila Keating in November 1997 described his dishes as "exquisitely complex", which she found was one of reasons for the first Michelin star (1994).

[49] Another reviewer of The Times in October 2003 praised Howard's "striking modern twists" on French classical cuisine, like "seared loin of venison with deep-fried quail's egg and a salad of beetroot and apple".

[68] One of The Square's co-owners, German-born Nigel Platts-Martin, whose father was an Army officer, attended The King's School, Canterbury and then the University of Oxford to study law.

[69][70] Later, he went on to work for law firms Freshfields Bruckhaus Deringer and S. G. Warburg & Co. before leaving to launch the restaurant Harveys in 1987 with its head chef Marco Pierre White.

[94] Based on a 2006 survey of 8,000 participants, Harden's named Platts-Martin's restaurant group as one of top three in London for "sheer consistency".

[98][100] On 8 January 2020, MARC was liquidated after the High Court of Justice granted the HM Revenue and Customs's petition filed on 6 November 2019.

[100][102] On 31 January 2020, property administrators abruptly closed The Square and another MARC-owned restaurant, Morton's Club during their lunch hours.

Nonetheless, McCormark appreciated Abela's efforts to run the "formal fine dining" restaurant, which "is an increasingly narrow and niche market".