The major third party in the UK is the Liberal Democrats.
In Scotland (which has a different political scene compared to the UK as a whole), the Greens are more the 4th party, on the same sort of scale as the Scottish Socialists. There Labour is top, but the Scottish National Party is breathing down their neck. The Tories are non-existent.
In Wales, Plaid Cymru is also an additional factor. I don't think the Greens have much representation beyond the very local level there either.
Basically the third UK party is the Liberal Democrats. I would classify them as intellectually leftist. It is not my impression that they have much of a base like Labour does - i.e. Unions etc. It leads them to have interesting positions - they support raising taxes to pay for socialised health care and they opposed the Iraq war but they support the integration of Europe and the adoption of the Euro (plus other pro-corporate policies).
Here is an interesting map (SNP, PC, UUP, SDLP, DP and SF are all non-England parties):
This doesn't tell you much about the Greens nationally, but it shows how they are locally-orientated.
The red section in the middle (where I live), is the non-London industrial sector - Manchester, Nottingham etc. Hence, Labour.
The blue swathes are Conservative areas, but have less seats to contest (so although it looks like they are huge, they're not).
Labour will blow the Tories out of the water next election unless at least a few of these things happen:
1. The Tories get a new leader.
2. Labour gets a "worse" leader (i.e. from the left-wing of the party, which would drive some media into the Tory camp)
3. Very low turn-out in Labour households.
4. Strong turn-out in Tories ones.
5. A Lib-Dem vote increase in Labour areas.
All 5 would probably have to happen in order for there to be a change of government come 2005/6 IMO.