Hi Mo and welcome,
The mower that you have is a Qualcast and would have had a Suffolk engine on it. They are a nice small mower and are generally quite easy to use. They have a two clutch system: the clutch leaver in the middle of the handlebars operates the main clutch (putting this into gear will start the cylinder) and the hand clutch is the land roll.
In terms of re powering, you will need to see if the crankshaft height and diameter will match the clutch centre. I am not sure if the boltholes in the mower will match the mounting pattern for the Honda - one of the others on the forum may be able to advise. Normally the Qualcast had captive nuts under the mounting holes however you can always drill new holes to suit.
Kind regards,
Sir Chook