Unfortunately the property is a couple of hours away from me so can't send a pic but from memory the newer plastic guttering isn't half-round as in the photo of the item you suggested. The actual profile isn't dis-similar to the rectangular profile of the existing wooden gutter but the join between the 2 is a bit of a bodge.
I think you have misunderstood what I was trying to get at. If you look at the profile of wooden troughing and the modern twin wall plastic troughing, the outside of the plastic troughing is the same shape as the timber troughing, i.e rectangular, whilst the profile of the gutter itself is half round:
When joining plastic to plastic sections a slide on sleeve piece like this is used:
This is slid onto the end of a length of troughing and the next piece of troughing is then slid into the end of the sleeve (the lighter=cpoloured area on the inside of the profile is a rubber sealing strip which is supplied loose with the component). The pieces are pilot drilled and screwed together using pan head stainless steel screws and all the joints are sealed with a coloured neutral cure silicone such as Dowsil 796.
When joining plastic to timber a different type of sleeve connector, called a half-lap connector, is used which slides over the end of the plastic troughing and is secured in place to that with stainless steel screws and silicone, as above. The half-round extension section should then sit inside the hollowed-out trough of the timber troughing and is siliconed and screwed in place to the timber, again as above. These half-lap connectors are handed, left hand and right hand (note the rubber seal):
When connecting into existing plastic troughing with new plastic troughing (such as in the middle of a terrace) it may be necessary to use a sleeve connector at one end (ideally the upper end on sloped runs) and a half-lap connector at the lower end
Sorry about the crappy photos, but I'm actually due to do this job on our house (plastic to plastic in my case) and whilst I have all the bits, I am missing a scaffolding tower which the hire shop failed to deliver on Friday. I should be able to demonstrate the plastic to timber connection technique next weekend (weather permitting, and providing the timber troughing comes off in one piece and doesn't just disintegrate as can happen) as well as post some better photos of the plastic components tomorrow, because I have them in stock and sitting in my garden shed right now