Don't know who told you, but they're talking bollocks to put it bluntly.
I/my dad have ran a 2L ghia mondy auto mk1 for around 7 years now.
When cold there is slight bit of 1st gear "hang" as it's called, but not to anything remotely like 4K, ours is around 1600/1700 rpm, once warm is fine.
Not changing into 4th(overdrive) is normal for yours, as the O/D light is used as a reporting feature for gearbox faults, that fact it is flashing shows it has a fault.
In your case it may be the usual stator(turbine) speed sensor issue, the plugs break on the sensor, the sensors go duff, around £50 fitted for a new one,(if mk1/2 mondy).
Then it may have another fault as well, the gear change points, when the stator speed sensor is working are electronically controlled by the control unit situated under the main large connector of lecky wires on the box, the good news is these are around £40 new, and a doddle to fit, no setting up, but when faulty these usually cause a massive issue with jumping up/down gears at any speed, rather than what you have.
The best thing you can do is to drive along to a auto box repairer who will drive your car and then give you a likely better definition than over the air so to speak, will save you money long tern.
tabetha