I had exactly the same cutting out at low speeds a couple of years ago, like pulling away from junctions or pottering around car parks etc. I looked at fuel, ignition etc. Eventually I found the culprit - the oxygen sensor, also known as the "lambda sensor." It was confirmed by my autosparks. He tested it - very simply as it only has three wires and they can be located up on the side of the wing inside the bonnet. You only need a voltmeter. With the car running, the volts should "scan" continuously from 0 - 4v. Anything else, and it's dead. The car will still run with a dead one but goes into "limp home" mode.
The sensor is screwed into the exhaust by the cat. It usually means getting that bit of the exhaust system off the car and heating it with an oxyacetaline burning torch to get it out if its an old one.
What me and my buddy did was to take it off and fit a non-cat exhaust temporarily to drive to Southport Jaguars who go the old sensor off using the method above and fitted the new one. The car ran all the way from Liverpool to Southport with no sensor at all fitted in "limp home" but got us there!
New sensors cost about £60. Virtually all cars made in the 1990's use the same Bosch type and don't even think of fitting a non-original one. Many Ebay sellers sell the Bosch units - just find your car in their "applications" list.
And the really good news - the new sensor totally transformed the performance, like a new engine! The performance must have been dropping off over the years (car bought in 2008) and you just don't notice.
We did think of having the sensors routinely tested at club meets - only takes minutes and crucial that you have a good one.
So definitely get it checked.
XJ6 3.2 1992
Range Rover 3.9 Vogue SE 1994
Austin A30 1955
Honda CB400A 1980