In an idle moment and as I live in central England, I downloaded the data aiming to play around with various ways of presenting it. For example, the Met Office shows each monthly mean temperature as a difference from the 1961-1990 mean (fig 1) which brings out the recent warm spell very well.
Only data from 1772 is used by the Met Office, as in Parker et al. (1992). By the way, the Parker paper highlights rather well the complexities and the adjustments made in compiling a long historical temperature record. It certainly isn't a list of thermometer readings.
However, if you simply plot the temperatures rather than the 1961-1990 differences (fig 2), the graph is rather more innocuous. After all, it's worth remembering that we experience daily and seasonal temperature changes far larger than those we are supposed to be alarmed about.
I see nothing wrong with either format. I'd use the Met Office approach if I had a reason to emphasise the recent warming spell. However, if I was wondering whether to move north to escape catastrophic warming, then I might use the simple temperature graph in fig 2.
The graph above (fig 3) is the CET data from 1979 - the satellite era. Just for fun I've fitted a second order polynomial which appears to show that the CET temperature has peaked, albeit a very shallow peak. I don't yet see it as a trend though, but it is worth noting how easy it is to present the data in many different ways depending at least in part on your agenda.
For example, the temperature record from 2006 plotted the Met Office way (fig 4) seems to show a rapid cooling trend. Maybe so, but as nobody knows where it will go in 2014, let alone the longer term, what conclusion do we draw from that? Don't try to build an agenda on temporary trends in cyclic phenomena is my conclusion - at the moment.
Finally, the month of June from 1659 to 2013 (fig 5) shows a flat linear trend over the entire three and a half centuries - h/t to sunshinehours for that oddity.