Personally, I’d not have come in via the Trafford route: too many water obstacles, and stuff like that, and you’d have had to take Liverpool first although they’d probably just let you in and the minidressed scousettes would just ride along on your tanks.
If Manchester was what you needed, then much better to seize the heights south and southeast round Stockport and Hazelgrove, possibly using airborne assault with portable artillery and mortars, plus the ring of hills from Bolton, Bury and Rochdale. To do both, too, you could just drive up the M6.
Then you have the entire city at your mercy from bombardment. Forget the “urban guerrillas” – too busy watching the telly. And from there you could just starve the place out.