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Wiktionary
give it some welly

alt. 1 (context UK English) To increase fuel or power to an engine, as to a car by depressing the gas pedal. 2 (context UK English) To apply great physical effort to (something). vb. 1 (context UK English) To increase fuel or power to an engine, as to a car by depressing the gas pedal. 2 (context UK English) To apply great physical effort to (something).

Usage examples of "give it some welly".

You could really give it some welly on that horse, he used to tell me.