How to Create privacy, in a rented garden?

It looks like the whole area has low fencing so there may not be anything you can do about it. First ask your landlord. You might be able to use expanding trellis (quite cheap) put along the top sideways, but it will need to have upright supports to hold it in place.

How about a big windbreak, the sort of thing one takes down to the beach....but just a bit higher and longer....you could then take it down and move it about just as you wanted.

Plastic pots, easy to move and not expensive then look for some climbers , if you put 4 canes in and tie the top you could grow sweet peas and black eyed susie, for example.
a popup gazebo on the patio would work too

Check your rent/lease agreement - there may well be restrictions on the height of any boundary. It looks like a fairly recent development and may have planning conditions. (I've just moved from a 1990s development where we weren't allowed any boundary structures at the front of the houses.)

In recent years it has been trendy to use triangles of brightly coloured sailcloth or similar, positioned overhead to keep off the sun. Could you erect something along the same lines but vertically, on eg a washing line pole, to screen the most prominent lines of sight?
I think that if it's portable or temporary, and in the back garden, it escapes planning restrictions - but I could be wrong!
Also, remember that a small barrier close-to has the same effect as a large barrier far-off, so it might be only necessary to address the seating area or living room window, for example.

Thank you for all the replies, I would be happy if I could just make a small private area in the back corner where the table is, the plant pot idea sounds nice and simple.

The collection of wheelie bins doesn't improve the view does it!? As you're renting it might be better to go for pots in general rather than planting in the ground and then possibly having to leave things behind before you get the best from them.

don't know if you can use this, but a lady I knew hung a large sheet on her clothesline, put her seating area behind it, and enjoyed privacy all summer...