PR is one of the key changes needed to make the UK a democratic country. No government since the war has had a majority of the popular vote and attempts by the voters to game the system with tactical voting are at best botched jobs.
See my comment here.
PR means that long-term issues can be tackled with much more consistency and pragmatism: and most of our current issues are long term, far longer term than any parliament or even run of parliaments under a new Thatcher or a new Blair. The NHS, housing, climate change and the economy all need planning on a time horizon of at least 50 years. By the time 50 years have gone by we will be in a world with a declining total population where even fewer younger people will be supporting even more older people. Five-year manifestos under the current system simply cannot do justice to problems of this order and timespan.
PR forces parties to combine in order to tackle real problems. The idea that first-past-the-post (FPP) is good because the electorate can chuck out a failing government is fundamentally flawed. It is like a family repeatedly throwing out the baby with the bath water and then wondering why its children have no long-term prospects. Governments do change under PR but the system often makes such change the equivalent of adjusting the route to broadly obvious destinations. FPP tends to deny the validity of the choice of existing destinations and then scraps the vehicle being used to get there. Good MPs of all parties have far more in common than they have differences to divide them; but FPP means that a faction that controls a minority can form a tail which wags the dog. Everyone but the faction loses.
Banderill's link to the Electoral Reform Society's information on proportional systems is a very good read. Any thorough-going proportional system is better than FPP but I think the Additional Member System (Germany, New Zealand and others) has much to recommend it because it retains an individual constituency MP whilst allowing into the legislature highly qualifiied people who do not happen to be natural doorstep campaigners.
If you feel like moving things forward,
Make Votes Matter is one organization that promotes fair voting and has no allegiance to any political party.