Check spark plugs, ignition coils, plug wire if either of these need change, last to doubt is fuel pump as you said it splutter while accelerating only.
If car recently went to mechanic and since then started spluttering, then check the spark plug gap. If all good, then check spark plug firing order. Hope it helps.
i am a owner of a freelander 2000 and have done 80,000 km my problem is that 5 weeks after buying the car I'm driving along the motorway at a steady 80 when suddenly all the power disappears & smoke starts to blow from the exhaust.