The Twinkle space telescope has been designed for the characterisation of exoplanets and Solar System objects. Operating in a low Earth, Sun-synchronous orbit, Twinkle is equipped with a 45 cm telescope and visible (0.4 - 1 μ m) and infrared (1.3 - 4.5 μ m) spectrometers which can be operated simultaneously. Twinkle is a general observatory which will provide on-demand observations of a wide variety of targets within wavelength ranges that are currently not accessible using other space telescopes or accessible only to oversubscribed observatories in the short-term future. Here we explore the ability of Twinkle's spectrometers to characterise the currently-known exoplanets. We study the spectral resolution achievable by combining multiple observations for various planetary and stellar types. We also simulate spectral retrievals for some well-known planets (HD 209458 b, GJ 3470 b and 55 Cnc e). From the exoplanets known today, we find that with a single transit or eclipse, Twinkle could probe 89 planets at low spectral resolution (R < 20) as well as 12 planets at higher resolution (R > 20) in channel 1 (1.3 - 4.5 μ m). With 10 observations, the atmospheres of 144 planets could be characterised with R <20 and 81 at higher resolutions. Upcoming surveys will reveal thousands of new exoplanets, many of which will be located within Twinkle's field of regard. TESS in particular is predicted to discover many targets around bright stars which will be suitable for follow-up observations. We include these anticipated planets and find that the number of planets Twinkle could observe in the near infrared in a single transit or eclipse increases R > 20. By stacking 10 transits, there are 1185 potential targets for study at R < 20 as well as 388 planets at higher resolutions. The majority of targets are found to be large gaseous planets although by stacking multiple observations smaller planets around bright stars (e.g. 55 Cnc e) could be observed with Twinkle. Photometry and low resolution spectroscopy with Twinkle will be useful to refine planetary, stellar and orbital parameters, monitor stellar activity through time and search for transit time and duration variations (TTVs and TDVs). Refinement of these parameters could be used to in the planning of observations with larger space-based observatories such as JWST and ARIEL. For planets orbiting very bright stars, Twinkle observations at higher spectral resolution will enable us to probe the chemical and thermal properties of an atmosphere. Simultaneous coverage across a wide wavelength range will reduce the degeneracies seen with Hubble and provide access to detections of a wide range molecules. There is the potential to revisit them many times over the mission lifetime to detect variations in cloud cover., (© The Author(s) 2018.)