If your XK120 is the same as the later saloon and it is electric, than you may have a bad otter switch. This is a switch mounted on the front of the water rail that is closed when the engine is cold so it sends power to the starting carb and send fuel to the engine. Once the engine is warm, this switch shuts off the power to the carb and the engine operates without the choke/carb. When the engine is hot/warm there is no need for the starting carb so the switch remains open until the engine cools to the point the choke is needed again. Many of us have wired a simple switch under the dash so that we can manually send power to the carb if needed to activate the carb if needed and the otter switch is still open.
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