I have just bought a 2002 Fiesta with the 1.3 Endura engine and 74,000 miles on the clock

After a short distance when pulling up in traffic, fumes are noticeable inside the car, that smell something like a cross between an exhaust or burning oil.

The smell goes after getting going again.

The car looks like it has had a recent exhaust change but there seems to be no obvious sign of a leak.

Has anybody got any other suggestions for things to look at

Sounds like you have an oil leak which is dripping onto the exhaust or manifold. It could be coming from anywhere, so you need to have a good look all over the engine. Most common places are the rocker cover gasket which should be easy to spot, or the oil pressure switch which is less easy but most likely if the oil is leaking down the front of the engine.If it is leaking from low down on either side of the engine then it could be the crankshaft oil seals. These normally go on older cars if the oil has been over filled. Also check the oil filter has been done up properly.

I would recommend checking the injector seals. I have seen it before where an old injector / spark plug seal has gone, fumes rise into the engine bay then get brought into the cabin...