Hi,
1080p is the resolution of the screen; The number "1080" represents 1,080 lines of vertical resolution and the p means progressive scan. The image is 1920×1080. Some TV sets will display at 1080p, others will take a 1080p and make it fit its highest resolution.
At 40 inch, you are better off going for a plasma TV if you want a better picture quality and not LCD - stick to LCD for 32 and below. Plasmas generate better pictures, and better blacks. If you can afford it, go for a pioneer or panasonic. The current latest panasonic TV's, offering full HD can be purchased from 500-750 pounds. (look at the Panasonic 42PZ80 range and the other in the family).
Before buying, make a list of any devices you will be using; dvd player, sky/freeview, consoles etc, and make sure the TV has enough inputs for them - or that they have compatible inputs (scart, dhmi, component etc).
If in doubt, dont be afraid to ask a local dealer for a picture demonstration (although be warned that they large chains often try to sell you the higher priced model over one with better quality picture).
EDIT:
You might also want to consider reading the following:
http://www.plasma-lcd-facts.co.uk/
and:
http://www.plasma-lcd-facts.co.uk/myths/response/
which should rule out any concerns about buying a plasma, such as myths like "burn in" and LCD lasting longer, which are not correct.