As other people have said there is no legal requirement for number of sockets, so trying to get your local authority to install more will be a long and exhausting exchange of words that may be very frustrating to say the least.
I would recommend going to B&Q, Homebase, Argos or simialr place (but not a poundland type of shop) and getting a few 2, 3 or 4 way extension leads to suit your needs. They come in several lenghts. Work out what you need, buy them and run the cable as neatly as you can round the edge of the room.
I would avoid the 3way square adaptor that plugs into the wall socket with NO LEAD, its just a big plug.
You can plug an extension lead into another without worrying. Its not perfect or pretty but it does the job.