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It's a Qualcast 51cm petrol S/P... supposedly with a B and S engine. About 3 years old.
XSZ51C-SD, The carb looks very much like the one in the video.
Briggs and Stratton 625e Series engine then, with a proper carb (albeit plastic) so no diaphragm. All you can really do is clean the carb as per the video. Wire strands are good for this, you don't need any fancy gadgets or jet brushes. If you have a spark, the engine kill must be working as intended, so no issue there. If it has a kill bar on the handle, tie it up so that you can concentrate on the rope pull better. I have had some success (mainly with 2 strokes admittedly) running a blow lamp across the plug to dry it out/ warm it up. Once you eventually get it going, it should start fine on subsequent fire ups. As said previously, pull the rope directly from the engine to get more revolutions per pull, not through the handle rope guide.
Only other thing I can think of, as it has a carb with a float bowl it has no primer bulb, so I assume it has auto choke. Try to see if this is working ok. It normally operates with a seperate rod connected to the top of the carb, and gradually turns back as it warms up. Shame you can't drill start it, that takes all the hard work out of it, although in saying that the choke still has to work. (Insert thumbs up smiley here when those evil Christmas smileys have gone)
Good luck.