Stutters and backfires when accelerating

Checked timing?

It could go either way. Stuttering and backfiring is one of 2 things:
1) raw fuel being dumped into the exhaust stream and being detonated.
2) spark too early or too late for valve timing.
Since timing is easiest to check, it's the first I mention. You said 'petrol'. I'm going to go out on a limb and say you aren't in the U.S. Is there somewhere you can rent or borrow a timing light? Or other tools?

The reason the engine seems to run fine at first is due to the cold start circuit. Less air is drawn into the engine, speeding up the idle during the warmup cycle. The increased engine speed adjusts the ignition timing. The computer will also adjust the timing during warmup.

I hope so. Let me know what you find out.