Clicking on the graph brings up a more detailed chart that allows comparison with other countries in the EU. We are, apparently, 7th in the list - behind Holland, Denmark, Luxembourg, Sweden, Germany and France. The source data is also available.
So there's one measure - connections per 100 inhabitants showing 30% penetration. Unhelpfully the next few entries only confuse the matter:
1) Of users connected to the Internet in December 2008, 95.1% are on broadband connections (the rest are (or were), it seems, on dialup.
2) In September 2009, 63% of households had broadband access (that is are connected to the broadband network rather than just have the potential to have such access - not immediately obvious from the text)
3)The UK ranks 5th for the number of fixed line broadband connections out of 33 countries with 18,827,500 subscribers. The US, Germany, Japan and France are ahead of us (who left out Holland, Denmark etc?)
4) The UK has 32 fixed broadband lines per 100 people, above the European average (and already higher than the google search result returned first), as of June 1st 2011. Indeed, between 2007 and 2010, connections above 10mbps went from 0 to 44.8%. One in eight has never used the Internet (Go, go race for online 2012!)
5) Ofcom said on 23rd August 2010 that "UK Broadband Penetration" was at 71%
6) In 2007 the UK was again 6th in a table with the US, China, Japan, Germany and South Korea ahead. Back then we had penetration of 23.1% or 13,957,111 subscribers.
Anyway ... I went with the first one.