It depends. In theory the screening may be regarded as street furniture, particularly if it is on free-standing feet or castors. However, some Local Planning Authorities (LPAs), such as Westminster City Council, will insist on a planning application and if the business is in a Conservation Area, planning permission will almost certainly be required. But in most areas they are less strict.
Planning guidelines for street cafes were relaxed after the first Covid lockdown to help the hospitality sector get back on its feet. The rules may be tightened up again soon, but may end up a little looser than before.
Some businesses work on the basis of ‘planning be damned’ – they install the screens and then wait to see what happens. Others will not take this risk and will contact their Local Planning Authority and ask for their advice.
There is a little known aspect of planning law which is that if a business does something which the planners claim is a breach of their permitted use, and prevent a business from doing that thing, if the business then applies for planning permission and it is granted, the LPA may be liable for any loss in profit they have caused.
Best advice is to make a preliminary enquiry with their LPA’s planning department. A preliminary enquiry won’t cost anything and this will clarify if an application is needed.
Finally, a structure of any kind is usually regarded as removable even if it is fixed in place (e.g. screens that are bolted down) as long as the structure can be unbolted and removed easily.