V8 disco cuts out when warm

Can anyone help please?
Other half has a v8 disco 1. It's already been used off road when he bought it so it's all set up. It started to cut out and lose all power so we changed the spider thinking that would cure it. It did to a degree as the power is still on. Replaced the fuel pump that wasn't working. Still cuts out. The relays click on and off like they should. It starts and runs until it gets up to temperature then cuts out, all electrics still on, then after a couple of mins starts again until it gets to temp. Driving us mad now cos it's just sat there. Tried to get it plugged in but nothing came up. Any ideas ?
Thanks

Have you looked at the ignition amplifier? I would suggest maybe a new amp and while you're at it maybe new dizzy cap and rotor arm but please buy genuine arm and cap, pattern parts just don't cut it.

Provided it can't be persuaded to keep running with throttle application:
As above, or coil praps?

Hi all. Had the same thing, start up fine, then cutting out when up to temp. After changing fuel pump(needed it), fuel filter, plugs, leads, dizzy cap, rotor arm, amp and coil. Still no joy. Bit the bullet and called out the AA. Turns out I have a Lucas opus 35DE8 dizzy that is known to fail on the hall sensor. It cracks with age and when the engine gets to temp, the ferrite pickup separates and without any warning the engine will just stop. No warning lights, nothing. Leave for 10/15 mins and it will run again until hot. As far as I could find out, there is no replacement unit for the sensor and the base plate is not in manufacture any more. You can buy a refurbished dizzy at many £££. But with a little more digging around other forums, Aston martin and Rolls Royce, I found out that you can remove the Lucas system and fit an optronic one instead for less £££. It's the Lumention PMA 50 and FK110 fitting kit for the the 35DE8. It took 20 mins to fit and the engine roared into life first turn of the key and has no problems so far, that was 2 weeks ago.
Of course, all of this is based on my engine troubles which is a 3.9 V8 EFI (14 CUX ECU).
Hope this helps in some way.