The company said rental levels between the start of October and the end of January had risen, underpinned by strong trading at stores over Christmas and the new year.
Shaftesbury said it wanted to capitalise on buoyant rental levels by re-letting vacant properties as soon as possible at higher rents.
Separately, footwear retailer Koko Shoes, one of the last remaining independents on Carnaby Street, has closed. Shaftesbury is now looking to fill the unit at number 1-2 Carnaby Street, which comprises 950 sq ft of ground floor space and a 1100 sq ft basement space.
Sports Direct owner Mike Ashley and a business partner are said to have built up as much as a 10% stake in the Shaftesbury business.