Green’s Dictionary of Slang

an attempt to find someone or something.

1974		G.F. Newman You Flash Bastard 38: ‘Bernard Hart? What d’you hear about him?’ There was a chance he might have known him. But didn’t. ‘Have a quiet punt around, he might be having something off. Some tom.’.
1983		J. Sullivan ‘Wanted’ Only Fools and Horses [TV script] I’ll have a cup of tea and have another punt round for him! Where can he be?