Guildhall Art Gallery, from 16 January 2015
One of the capital’s hidden gems, the Guildhall Art Gallery, has been given some extra sparkle. A refurbishment and rehang is complete, with highlights including Pre-Raphaelite works by Dante Gabriel Rossetti and John Everett Millais PRA. Anyone who likes Victorian art should make their acquaintance with the gallery, which draws its displays from the City of London’s art collection.

Bloomberg Space, London 16 January–15 March 2015
After visiting the Guildhall, walk up Moorgate to Finsbury Square to one of the City’s galleries dedicated to contemporary art, Bloomberg Space. Their rotating programme of (normally solo) exhibitions alights this week on Adam Dant, an artist whose idiosyncratic drawings map connections between people and places. His attention here shifts to Budge Row, a once bustling City street that no longer exists: a huge sepia ink drawing draws together in one image the thoroughfare’s historical and contemporary threads.

Breese Little, London, 16 January–21 February 2015
And after the Bloomberg Space, one can walk 15 minutes west to Clerkenwell’s Breese Little gallery, which is presenting a group exhibition that includes works by RA Schools alumni Charlie Billingham and Aimée Parrott. The show’s title ‘Promise of Palm Trees’ is appropriate for the alluring but ultimately elusive nature of the paintings on view.

White Cube, Mason’s Yard, London, 16 January–14 March 2015
From palm trees in Clerkenwell to spruces in St James’s, in the form Virginia Overton’s installation of whitewood at White Cube. In the gallery’s ground floor gallery, huge planks of timber are held in tension while curving between floor and ceiling. The exhibition is Overton’s first solo show in the UK, and this installation, together with other site-specific sculptures on view, form a perfect introduction to the American artist’s playfulness with material, architecture and physical force.

Business Design Centre, London, 21–25 January 2015
But if going from gallery to gallery this week seems too tough, then visit 128 galleries under one roof at the Business Design Centre, which hosts the London Art Fair once again. The fair’s has a strong reputation when it comes to Modern British art (both pre- and post-war), so this year it has invited Chichester’s Pallant House gallery to show its superb collection of works by figures such as Barbara Hepworth, Lucian Freud and Patrick Caulfield RA.

Sam Phillips (@SamP_London) is Editor of RA Magazine.