Actually, the name of the party is the Social and Liberal Democrats. Apparently they wanted to be known as the “Social Democrats” when they first made that name, but the phrase “liberal democrat” caught on instead. And yes, they are now probably the most left-wing of the British parties, but this may change.
See, when the Libs. were founded, the Labour party was still hard-core socialist. They weren’t quite- not quite- advocating communism, but they weren’t far off, either. The 1983 Labour manifesto (known to some as “the longest suicide note in history”) proposed, among other things, complete and unilateral nuclear disarmament and the nationalisation of all key industries, from heavy manufacturing to services like transport. In response to the hard-left and unpopular Labour position, four Labour MPs left to found the SDP, which later merged with the Liberals. They were supposed to be centre-ground, breaking the mould of adverserial British politics, and offering, basically, what New Labour and the Conservatives are both struggling to offer now- management, rather than ideology.
Unfortunately for the SDP, after they started making real electoral progress (becoming, at one point, the effective opposition party), both the Conservatives and Labour began to re-organise and try to offer less divisive, centre-ground politics. The Conservatives ditched Thatcher, Labour got Blair, and both moved back into the centre ground (Labour, for example, ditched “Clause IV”, which had been party of the Labour Party Constitution, and basically promised they would try to bring socialism). This left the Liberals out in the cold, so they moved left, to pick up the voters that Labour had left behind by cosying up to big business and so forth. This led to the current liberals, who are definitely left of Blair, but may not be to the left of the rest of the Labour party.
In case you didn’t know, Blair has recently had great difficulty forcing through his Conservative-esque education reforms, and the majority of the (still strongly left-wing) Labour MPs, many of whom have Scottish or Welsh seats (both of whose constituents have very socialist tendencies) are grumbling and hoping that Blair will resign so they can get a more left-wing PM. At the same time, the Lib Dems have recently voted in a new leader (Sir Menzies Campbell), who is widely seen as a caretaker while the party undergoes an ideological struggle about which direction to go in now that the Centre may be opening up again. At the same time the new Tory leader, Campbell, is trying to move his party back to the centre and make them electable, possibly opening up the possibility of a more libertarian-style Lib Dem party co-operating with the Conservatives in the event of parliamentary instability.
There. More than you ever needed or wanted to know about the Lib Dems.
Oh, and there is still a dihictomy in the Liberals between the remains of the old Liberal party, whose concerns centre on civil liberties, over-regulation and so on, and the Labour defectors, who are mainly concerned with social justice policies (NHS etc.). The party has MPS and members of both stripes, and sometimes they agree (over the enviroment or the Iraq war*, for example.) They are also the only strongly-pro-Europe party, which is a somewhat unpopular position to take.
*Which is hugely unpopular here, far outstripping even the very worst American opposition. Both before and after, there have been millions who turned out to protest British involvement. The Iraq war is widely credited with lowering Blair’s majority from 179 to 60-odd. Without it, he probably could have won a third landslide victory.