Dan, Brockhouse bought BMB in the 1940’s. BMB imported Simplicity two wheeled garden tractors from America and sold them in the UK as, Hoemate, Cultmate and Plowmate. Early Hoemate had a Brockhouse Spryt 2 stroke engine.
To remove the inner from the slide slacken off the adjusters completely on both the carb and the throttle lever. Remove inner from lever. You should then be able to push the inner into the slide far enough to get the nipple on the end out; note there is a spring in the slide. If the inner is frayed you will need to replace it. Probably best to speak to John Cruse at The Mower Centre, Hailsham, he can supply a complete cable the correct length if you give him the details.
A few questions.
You say you cannot remove inner from carb, why?
How is inner attached to carb?
How is inner attached to throttle lever?
Inner cables usually terminate at both ends with a nipple that is soldered on. A photo of your engine and throttle would help.
